messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 24
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{17}$\n$x \\equiv 6 \\pmod{4}$\n$x \\equiv 2 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$170$"
... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 10 \\pmod{4}$\n$x \\equiv 18 \\pmod{13}$"
},
{
"role": "assistant",
"content": "$18$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 17 \\pmod{17}$\n$x \\equiv 17 \\pmod{19}$\n$x \\equiv 10 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$34... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 20 \\pmod{3}$\n$x \\equiv 16 \\pmod{5}$\n$x \\equiv 4 \\pmod{8}$"
},
{
"role": "assistant",
"content": "$116$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 12 \\pmod{4}$\n$x \\equiv 12 \\pmod{16}$"
},
{
"role": "assistant",
"content": "$12$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 5 \\pmod{14}$\n$x \\equiv 5 \\pmod{15}$"
},
{
"role": "assistant",
"content": "$5$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 20 \\pmod{19}$\n$x \\equiv 17 \\pmod{20}$"
},
{
"role": "assistant",
"content": "$77$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 19 \\pmod{5}$\n$x \\equiv 12 \\pmod{13}$\n$x \\equiv 6 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$584... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{9}$\n$x \\equiv 11 \\pmod{7}$\n$x \\equiv 4 \\pmod{5}$"
},
{
"role": "assistant",
"content": "$179$"
... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 9 \\pmod{17}$\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 15 \\pmod{16}$"
},
{
"role": "assistant",
"content": "$174... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 17 \\pmod{3}$\n$x \\equiv 6 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$23$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 15 \\pmod{19}$\n$x \\equiv 5 \\pmod{9}$\n$x \\equiv 17 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$1193... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{7}$\n$x \\equiv 12 \\pmod{11}$"
},
{
"role": "assistant",
"content": "$56$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 7 \\pmod{11}$\n$x \\equiv 0 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$18$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{9}$\n$x \\equiv 8 \\pmod{10}$\n$x \\equiv 13 \\pmod{5}$"
},
{
"role": "assistant",
"content": "$68$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 4 \\pmod{3}$\n$x \\equiv 19 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$19$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 18 \\pmod{10}$\n$x \\equiv 8 \\pmod{13}$"
},
{
"role": "assistant",
"content": "$8$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{13}$\n$x \\equiv 17 \\pmod{20}$\n$x \\equiv 7 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$1197... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 12 \\pmod{16}$\n$x \\equiv 19 \\pmod{17}$\n$x \\equiv 6 \\pmod{2}$"
},
{
"role": "assistant",
"content": "$172... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 13 \\pmod{17}$\n$x \\equiv 15 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$81$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{8}$\n$x \\equiv 3 \\pmod{11}$\n$x \\equiv 0 \\pmod{20}$"
},
{
"role": "assistant",
"content": "$80$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 12 \\pmod{4}$\n$x \\equiv 3 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$20$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{12}$\n$x \\equiv 7 \\pmod{19}$"
},
{
"role": "assistant",
"content": "$140$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 5 \\pmod{5}$\n$x \\equiv 18 \\pmod{18}$\n$x \\equiv 11 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$270$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 11 \\pmod{9}$\n$x \\equiv 16 \\pmod{5}$\n$x \\equiv 2 \\pmod{14}$"
},
{
"role": "assistant",
"content": "$506$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 20 \\pmod{9}$\n$x \\equiv 2 \\pmod{13}$\n$x \\equiv 4 \\pmod{2}$"
},
{
"role": "assistant",
"content": "$2$"
... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{13}$\n$x \\equiv 8 \\pmod{10}$\n$x \\equiv 8 \\pmod{10}$\n$x \\equiv 14 \\pmod{7}$"
},
{
"role": "assist... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{2}$\n$x \\equiv 4 \\pmod{4}$\n$x \\equiv 0 \\pmod{8}$\n$x \\equiv 13 \\pmod{7}$"
},
{
"role": "assistant"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{5}$\n$x \\equiv 15 \\pmod{6}$\n$x \\equiv 15 \\pmod{12}$\n$x \\equiv 17 \\pmod{19}$"
},
{
"role": "assis... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 9 \\pmod{16}$\n$x \\equiv 9 \\pmod{2}$"
},
{
"role": "assistant",
"content": "$9$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{10}$\n$x \\equiv 17 \\pmod{13}$\n$x \\equiv 11 \\pmod{15}$\n$x \\equiv 5 \\pmod{3}$"
},
{
"role": "assis... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 10 \\pmod{3}$\n$x \\equiv 5 \\pmod{11}$"
},
{
"role": "assistant",
"content": "$16$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{15}$\n$x \\equiv 18 \\pmod{5}$\n$x \\equiv 2 \\pmod{8}$\n$x \\equiv 12 \\pmod{14}$"
},
{
"role": "assista... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 11 \\pmod{9}$\n$x \\equiv 10 \\pmod{2}$"
},
{
"role": "assistant",
"content": "$2$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{4}$\n$x \\equiv 11 \\pmod{2}$"
},
{
"role": "assistant",
"content": "$3$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 9 \\pmod{18}$\n$x \\equiv 1 \\pmod{13}$\n$x \\equiv 15 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$729... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 20 \\pmod{15}$\n$x \\equiv 5 \\pmod{3}$\n$x \\equiv 10 \\pmod{4}$"
},
{
"role": "assistant",
"content": "$50$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{14}$\n$x \\equiv 7 \\pmod{10}$\n$x \\equiv 4 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$157$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{3}$\n$x \\equiv 20 \\pmod{11}$\n$x \\equiv 16 \\pmod{2}$\n$x \\equiv 14 \\pmod{17}$"
},
{
"role": "assist... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{16}$\n$x \\equiv 1 \\pmod{10}$"
},
{
"role": "assistant",
"content": "$1$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{11}$\n$x \\equiv 7 \\pmod{4}$\n$x \\equiv 9 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$107$"
... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 10 \\pmod{7}$\n$x \\equiv 12 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$3$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{8}$\n$x \\equiv 16 \\pmod{4}$\n$x \\equiv 18 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$120... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 12 \\pmod{16}$\n$x \\equiv 3 \\pmod{13}$\n$x \\equiv 5 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$796$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 17 \\pmod{8}$\n$x \\equiv 6 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$9$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 19 \\pmod{2}$\n$x \\equiv 18 \\pmod{9}$"
},
{
"role": "assistant",
"content": "$9$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 12 \\pmod{20}$\n$x \\equiv 14 \\pmod{19}$"
},
{
"role": "assistant",
"content": "$52$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 15 \\pmod{19}$\n$x \\equiv 0 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$91$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 9 \\pmod{4}$\n$x \\equiv 1 \\pmod{13}$"
},
{
"role": "assistant",
"content": "$1$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 15 \\pmod{18}$\n$x \\equiv 15 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$15$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 18 \\pmod{8}$\n$x \\equiv 15 \\pmod{5}$"
},
{
"role": "assistant",
"content": "$10$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 13 \\pmod{17}$\n$x \\equiv 6 \\pmod{11}$\n$x \\equiv 0 \\pmod{5}$"
},
{
"role": "assistant",
"content": "$710$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 5 \\pmod{6}$\n$x \\equiv 11 \\pmod{19}$"
},
{
"role": "assistant",
"content": "$11$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{16}$\n$x \\equiv 16 \\pmod{13}$\n$x \\equiv 13 \\pmod{4}$\n$x \\equiv 3 \\pmod{2}$"
},
{
"role": "assista... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 9 \\pmod{13}$\n$x \\equiv 10 \\pmod{2}$\n$x \\equiv 20 \\pmod{11}$\n$x \\equiv 19 \\pmod{9}$"
},
{
"role": "assist... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{19}$\n$x \\equiv 10 \\pmod{2}$"
},
{
"role": "assistant",
"content": "$20$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{17}$\n$x \\equiv 8 \\pmod{15}$"
},
{
"role": "assistant",
"content": "$173$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 20 \\pmod{19}$\n$x \\equiv 3 \\pmod{4}$"
},
{
"role": "assistant",
"content": "$39$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{12}$\n$x \\equiv 1 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$1$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 10 \\pmod{19}$\n$x \\equiv 20 \\pmod{10}$\n$x \\equiv 0 \\pmod{15}$"
},
{
"role": "assistant",
"content": "$39... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 18 \\pmod{9}$\n$x \\equiv 2 \\pmod{11}$\n$x \\equiv 12 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$90$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{16}$\n$x \\equiv 15 \\pmod{15}$\n$x \\equiv 18 \\pmod{3}$\n$x \\equiv 12 \\pmod{9}$"
},
{
"role": "assis... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 4 \\pmod{19}$\n$x \\equiv 11 \\pmod{10}$\n$x \\equiv 5 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$251$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 4 \\pmod{16}$\n$x \\equiv 11 \\pmod{11}$\n$x \\equiv 12 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$25... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 2 \\pmod{17}$\n$x \\equiv 5 \\pmod{10}$"
},
{
"role": "assistant",
"content": "$155$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{15}$\n$x \\equiv 17 \\pmod{11}$"
},
{
"role": "assistant",
"content": "$61$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 11 \\pmod{18}$\n$x \\equiv 5 \\pmod{19}$"
},
{
"role": "assistant",
"content": "$119$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 4 \\pmod{4}$\n$x \\equiv 6 \\pmod{14}$"
},
{
"role": "assistant",
"content": "$20$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 13 \\pmod{5}$\n$x \\equiv 6 \\pmod{6}$\n$x \\equiv 8 \\pmod{16}$"
},
{
"role": "assistant",
"content": "$168$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{7}$\n$x \\equiv 11 \\pmod{8}$"
},
{
"role": "assistant",
"content": "$35$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{11}$\n$x \\equiv 13 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$25$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{19}$\n$x \\equiv 9 \\pmod{16}$"
},
{
"role": "assistant",
"content": "$217$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 6 \\pmod{6}$\n$x \\equiv 18 \\pmod{14}$\n$x \\equiv 16 \\pmod{5}$\n$x \\equiv 1 \\pmod{11}$"
},
{
"role": "assista... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{13}$\n$x \\equiv 7 \\pmod{4}$\n$x \\equiv 8 \\pmod{19}$\n$x \\equiv 10 \\pmod{3}$"
},
{
"role": "assistan... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{3}$\n$x \\equiv 14 \\pmod{13}$"
},
{
"role": "assistant",
"content": "$14$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 19 \\pmod{13}$\n$x \\equiv 15 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$71$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 10 \\pmod{5}$\n$x \\equiv 15 \\pmod{20}$\n$x \\equiv 3 \\pmod{3}$\n$x \\equiv 6 \\pmod{17}$"
},
{
"role": "assista... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{11}$\n$x \\equiv 14 \\pmod{16}$"
},
{
"role": "assistant",
"content": "$14$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{16}$\n$x \\equiv 15 \\pmod{9}$"
},
{
"role": "assistant",
"content": "$96$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 19 \\pmod{10}$\n$x \\equiv 3 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$59$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 4 \\pmod{20}$\n$x \\equiv 7 \\pmod{9}$"
},
{
"role": "assistant",
"content": "$124$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 3 \\pmod{16}$\n$x \\equiv 7 \\pmod{3}$\n$x \\equiv 5 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$787$"... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 4 \\pmod{8}$\n$x \\equiv 14 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$28$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 10 \\pmod{13}$\n$x \\equiv 8 \\pmod{17}$"
},
{
"role": "assistant",
"content": "$127$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{19}$\n$x \\equiv 11 \\pmod{3}$"
},
{
"role": "assistant",
"content": "$35$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 19 \\pmod{16}$\n$x \\equiv 20 \\pmod{7}$"
},
{
"role": "assistant",
"content": "$83$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 13 \\pmod{19}$\n$x \\equiv 9 \\pmod{10}$"
},
{
"role": "assistant",
"content": "$89$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 16 \\pmod{11}$\n$x \\equiv 1 \\pmod{10}$\n$x \\equiv 11 \\pmod{20}$"
},
{
"role": "assistant",
"content": "$71... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{18}$\n$x \\equiv 4 \\pmod{19}$\n$x \\equiv 18 \\pmod{8}$"
},
{
"role": "assistant",
"content": "$954$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 18 \\pmod{13}$\n$x \\equiv 5 \\pmod{5}$"
},
{
"role": "assistant",
"content": "$5$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 13 \\pmod{14}$\n$x \\equiv 13 \\pmod{15}$"
},
{
"role": "assistant",
"content": "$13$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 19 \\pmod{3}$\n$x \\equiv 8 \\pmod{14}$"
},
{
"role": "assistant",
"content": "$22$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 5 \\pmod{4}$\n$x \\equiv 16 \\pmod{19}$\n$x \\equiv 16 \\pmod{15}$"
},
{
"role": "assistant",
"content": "$301... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 17 \\pmod{5}$\n$x \\equiv 15 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$27$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 1 \\pmod{14}$\n$x \\equiv 17 \\pmod{9}$"
},
{
"role": "assistant",
"content": "$71$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 8 \\pmod{19}$\n$x \\equiv 20 \\pmod{7}$\n$x \\equiv 0 \\pmod{6}$\n$x \\equiv 5 \\pmod{11}$"
},
{
"role": "assistan... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{17}$\n$x \\equiv 20 \\pmod{14}$\n$x \\equiv 19 \\pmod{5}$"
},
{
"role": "assistant",
"content": "$34$... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{7}$\n$x \\equiv 14 \\pmod{3}$\n$x \\equiv 5 \\pmod{6}$"
},
{
"role": "assistant",
"content": "$35$"
... | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 0 \\pmod{3}$\n$x \\equiv 18 \\pmod{10}$"
},
{
"role": "assistant",
"content": "$18$"
}
] | number_theory | chinese_remainder_theorem |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{8}$\n$x \\equiv 8 \\pmod{18}$\n$x \\equiv 8 \\pmod{6}$\n$x \\equiv 13 \\pmod{17}$"
},
{
"role": "assista... | number_theory | chinese_remainder_theorem |
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