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I have a three pairs of points namely : p{1,1} p{1,2} p{2,1} p{2,2} p{3,1} p{3,2}, I want to find p such that : |p-p{i,1}| = |p-p{i,2}| for all i. I know that these represent three planes, but I am not sure whether these planes do meet in a single point. My simple question is even if the three planes are not parallel d... |
How to determine a point in R3 which is which is equidistant to three pairs of point ? |
"What else can you count with these?": Solutions to the Fermat equation $x^n + y^n = z^n$. (If this doesn't make immediate sense, I will add more material later, when I have more time.) |
A triple of positive integers $(a,b,c)$ is an $abc$-triple if $a$ and $b$ are coprime and $c = a + b$. Define the _quality_ or _power_ of an $abc$-triple as $P(a,b,c) = \frac{\log c}{\log \text{rad}(abc)}$, where $\text{rad}(k)$ denotes the product of distinct prime divisors of $k$.
One version of the $abc$-Conject... |
Greetings.
$$\sum_{i=x}^{2x} 5 - \sum_{k=2x+1}^{5x+1} 5 = -25$$
How can I discover the value of X?
Thanks in advance! |
Greetings.
$$\sum_{i=x}^{2x} 5 - \sum_{k=2x+1}^{5x+2} 5 = -25$$
How can I discover the value of X?
Thanks in advance!
EDIT: Turns out it was 5x+2, not 5x+1. My bad, apologies for the trouble. |
$$\sum_{i=1}^{x} x + \sum_{i=1}^{x} 2 = 8$$
Trying to discover $x$ here, so I made:
$$x(x-1) + 2(x-1) = 8$$
Which should give me the $x$, but instead of an integer I get:
$$x = \frac{-1\pm\sqrt{41}}{2}$$
When the answer should be $x=2$, according to the solution.
What am I doing wrong? |
One important fact that ought to be mentioned explicitly is that
$$\frac{d \sin x}{dx} = \cos x$$
*only when $x$ is measured in radians.*
For a general angle measure, the derivative of $\sin x$ is some scalar multiple of $\cos x$. In fact, it could be argued that this is the [major reason for the usefulness of... |
Rearrange the formula for the sum of a geometric series to find "r"? |
Consider the set $F_n: = [n]^{[n]}$ of all functions $f:[n] \rightarrow [n]$, $[n] = \lbrace 1,2,...,n\rbrace$. It is well known that $|F_n| = n^n$.
**Edit**: Let two functions $f, g$ in $F_n$ be of the same isomorphism type ($f\sim g$) iff there exists a permutation $\pi$ such that $f\pi = \pi g $
> What is the... |
I think the best approach is to start by considering what $X(4) = 5$ actually means. It means that through the first four months of the year there have been 5 claims. Denote this event $D$. Given that, you're looking for the probability that all three of the following events occurred:
1. Exactly 3 claims in the ... |
Please imagine that we have a circular segment with some arc length 's' and chord length 'a' (using notation from http://mathworld.wolfram.com/CircularSegment.html).
Provided only 'a' and 's', and placing the left-hand-side point of the chord at the origin of the Euclidean plane (or a more convenient point), is th... |
Please imagine that we have a circular segment with some arc length 's' and chord length 'a' (using notation from http://mathworld.wolfram.com/CircularSegment.html).
Provided only 'a' and 's', and placing the left-hand-side point of the chord at the origin of the Euclidean plane (or a more convenient point), is th... |
Let $\{a_k\}$, $\{b_k\}$ be two sequences in $\mathbb{R}$. Suppose $\{a_k\}$ converges to $a$ s.t. $\liminf_{k \to \infty} {a_k} = \lim_{k \to \infty} {a_k} = a$.
Is it then true that $\liminf_{k \to \infty} (a_k - b_k) = \lim_{k \to \infty} a_k + \liminf_{k \to \infty} -b_k$? |
Please imagine that we have a circular segment with some arc length 's' and chord length 'a' (using notation from http://mathworld.wolfram.com/CircularSegment.html).
Provided only 'a' and 's', and placing the left-hand-side point of the chord at the origin of the Euclidean plane (or a more convenient point), is th... |
I think the best approach is to start by considering what $X(4) = 5$ actually means. It means that through the first four months of the year there have been 5 claims. Denote this event $D$. Given that, you're looking for the probability that all three of the following events occurred:
1. Exactly 3 claims in the ... |
As an addendum, you can download the Mathematica notebook from <a href="http://demonstrations.wolfram.com/GraphingDerivatives/">Graphing Derivatives</a>, which allows you to play a little bit with $\text{sin}(x)$, $\text{cos}(x)$ and another function. I think it shows a very obvious but interesting construction of thos... |
As an addendum, you can download the Mathematica notebook from <a href="http://demonstrations.wolfram.com/GraphingDerivatives/">Graphing Derivatives</a>, which allows you to play a little bit with $\text{sin}(x)$, $\text{cos}(x)$ and another function. I think it shows a very obvious but interesting construction of thos... |
summation from 2 to infty $(-1)^n(n^2)(ln(n))^(-n))$ Divergent? |
$\sum\limits_{2}^{\infty} (-1)^n(n^2)(ln(n))^{-n}$ divergent? |
$\sum\limits_{n=2}^{\infty} (-1)^n(n^2)(ln(n))^{-n}$ divergent? |
If $a_n$ is a sequence, then $\lim_{n\to\infty}a_n = 0$ if and only if $\lim_{n\to\infty} |a_n| = 0$. So if the absolute value of the terms does not go to zero, then the terms don't go to zero.
In other words, if you know that $\lim \frac{n}{\ln (n)}\neq 0$, then it follows that $\lim\frac{(-1)^n n}{\ln n}\neq 0$. (... |
If $a_n$ is a sequence, then $\lim_{n\to\infty}a_n = 0$ if and only if $\lim_{n\to\infty} |a_n| = 0$. So if the absolute value of the terms does not go to zero, then the terms don't go to zero.
In other words, if you know that $\lim \frac{n}{\ln (n)}\neq 0$, then it follows that $\lim\frac{(-1)^n n}{\ln n}\neq 0$. (... |
Is $\sum\limits_{n=2}^{\infty} \frac{(-1)^n n^2}{( \ln(n))^n}$ divergent? |
Let G be a graph and δ(G) the minimum degree of a peak. Describe an algorithm in pseudocode that, for a given tree T with k<= δ(G) edges, should be build (in polinomial time) a sub-graph H of G so that H is isomorphic with T.
How do I even start ? |
This may sound silly, but... Suppose an aspiring amateur mathematician wanted to plan to move to another city...
What are some cities that are home to some of the largest number of the brightest mathematicians? I'm sure this may depend on university presence, or possibly industry presence, or possibly something surp... |
Is the subset consisting of all integrable(or square integrable) smooth functions of the set of all integrable (or square integrable) functions dense under the usual euclidean or integral of absolute difference metric ?
by smooth i mean derivatives of all orders exit.
- Rajesh.D |
Are the smooth functions dense in either L^2 or L^1? |
You are asking for which $N$ there is an element of norm
$N$ in the quadratic ring $R=\mathbb{Z}[\sqrt{94}]$.
Now $R$ is the full ring of integers in the field
$\mathbb{Q}(\sqrt{94})$ which has class number one.
The problem is almost the same as determining for which
$N$ there is a norm $N$ ideal in $R$. There is ... |
Given a continuous function $g$ on $\mathbb R$. Is it possible to decompose $\mathbb R$ as the union of a countable collection of intervals $I_n=]a_n, a_{n+1}]$ so that $g$ is monotone on each $I_n$?
The same question may be asked for a continuous function defined on a bounded interval. |
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-\exp(\frac{2}{3}\pi\cdot i)) \cdot \Gamma(-\exp(\frac{4}{3}\pi \cdot i))} $$ is, at $x = 0$. I'm also interested in the method behind computing the expansion series.
You might think: "why do... |
What is the Expansion Series of the following function? |
What is the Series Expansion of the following function? |
I am a soon-to-be high school graduate with inclination towards mathematics. I enjoy doing math, and am relatively good at it, but I dislike the way I am being taught. I feel like I am being taught methods for solving a lot of problems, but I don't see how any of this fits together.
I was considering pursuing a care... |
Suppose $f(x,y) = c$ for $0<y<x<1$ and 0 outside. What is $P(X+Y \leq 1)$? What is $P(X^2+Y^2 \leq 1)$?
So $P(X+Y \leq 1) = $\int_{0}^{1} \int_{0}^{1-x} 2 \ dy \ dx$? Likewise, $P(X^2+Y^2 \leq 1) = \int_{0}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} 2 \ dy \ dx$? This is assuming that $c=2$.
|
Suppose $f(x,y) = c$ for $0\lt y\lt x\lt 1$ and 0 outside. What is $P(X+Y \leq 1)$? What is $P(X^2+Y^2 \leq 1)$?
So $P(X+Y \leq 1) = \int_{0}^{1} \int_{0}^{1-x} 2 \ dy \ dx$? Likewise, $P(X^2+Y^2 \leq 1) = \int_{0}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} 2 \ dy \ dx$? This is assuming that $c=2$.
|
Suppose $f(x,y) = c$ for $0\lt y\lt x\lt 1$ and $0$ outside. What is $P(X+Y \leq 1)$? What is $P(X^2+Y^2 \leq 1)$?
So $P(X+Y \leq 1) = \int_{0}^{1} \int_{0}^{1-x} 2 \ dy \ dx$? Likewise, $P(X^2+Y^2 \leq 1) = \int_{0}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} 2 \ dy \ dx$? This is assuming that $c=2$.
|
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-(\exp(\frac{2}{3}\pi\cdot i))x) \cdot \Gamma(-(\exp(\frac{4}{3}\pi \cdot i))x)} $$ is, at $x = 0$. I'm also interested in the method behind computing the expansion series.
You might think: "... |
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-(\exp(\frac{2}{3}\pi\cdot i))x) \cdot \Gamma(-(\exp(\frac{4}{3}\pi \cdot i))x)} $$ is, at $x = 0$. I'm also interested in the method behind computing the expansion series.
You might think: "... |
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-(\exp(\frac{2}{3}\pi\cdot i))x) \cdot \Gamma(-(\exp(\frac{4}{3}\pi \cdot i))x)} $$ is, at $x = 0$. I'm also interested in the method behind computing the expansion series.
You might think: "... |
Many young, and not so young, mathematicians struggle with how to spend their time. Perhaps this is due to the 90%-10% rule for mathematical insight: 90 pages of work yield only 10 pages of useful ideas. A venerable mathematician once described his career to me as constantly stumbling around in the dark. Of cours... |
What is your method? |
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-(\exp(\frac{2}{3}\pi\cdot i))x) \cdot \Gamma(-(\exp(\frac{4}{3}\pi \cdot i))x)} $$ is, at $x = 0$. I'm also interested in the method behind computing the series expansion.
You might think: "... |
Many young, and not so young, mathematicians struggle with how to spend their time. Perhaps this is due to the 90%-10% rule for mathematical insight: 90 pages of work yield only 10 pages of useful ideas. A venerable mathematician once described his career to me as constantly stumbling around in the dark. Of cours... |
Suppose R=S/I is the homomorphic image of a local Cohen-Macaulay ring (S,m). I know the completion of R as an S-module is the just R \otimes S^, where S^=the m-adic completion of S. Is this also the completion of R as a ring? (I think this comes down to showing that the inverse limit of S/(m^i +I) is the same as the ... |
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-(\exp(\frac{2}{3}\pi\cdot i))x) \cdot \Gamma(-(\exp(\frac{4}{3}\pi \cdot i))x)} $$ is, at $x = 0$. I'm also interested in the method behind computing the series expansion.
You might think: "... |
I was wondering what the expansion series of the function
$$ f(x) = -\frac{1}{x^3} \cdot \frac{1}{\Gamma(x) \cdot \Gamma(-(\exp(\frac{2}{3}\pi\cdot i))x) \cdot \Gamma(-(\exp(\frac{4}{3}\pi \cdot i))x)} $$ is, at $x = 0$. I'm also interested in the method behind computing the series expansion.
You might think: "... |
I've wasted a few days trying to prove Thue's lemma with no success! The proof is absolutely easy if you just count. What 'red flags' do are useful to give you a warning that counting might be more productive than other approaches?
I can start with one point, but it's more of a conceptual one and requires you to see... |
Learning When to count? |
I've wasted a few days trying to prove Thue's lemma with no success! The proof is absolutely easy if you just count. What 'red flags' are useful to give you a warning that counting might be more productive than other approaches?
I can start with one point, but it's more of a conceptual one and requires you to see th... |
Many young, and not so young, mathematicians struggle with how to spend their time. Perhaps this is due to the 90%-10% rule for mathematical insight: 90 pages of work yield only 10 pages of useful ideas. A venerable mathematician once described his career to me as constantly stumbling around in the dark. Of cours... |
thanks for your re-edit...now it makes much more sense and you are right, much cleaner!
Since I was last working on the problem, I have come up with the following alternative solution which yields the same numerical answer as you:
P{X(2) = 3, X(3) = 5 | X(4) = 5}
= P{X(2) = 3, X(3) = 5, X(4) = 5} / P{X(4) =... |
$$\sum_{n,\geq0} ({\frac{2}{3}})^{2n-1}$$
I managed to find that this is a geometric series with common ratio of $4/9$, therefore convergent. That means it's possible to calculate the sum of the series. Can I get any tip of how to do the sum of any kind of geometric series that converge? I've been researching, but a... |
$$\sum_{n,\geq0} ({\frac{2}{3}})^{2n-1}$$
I managed to find that this is a geometric series with common ratio of $4/9$, therefore convergent. That means it's possible to calculate the sum of the series. Can I get any tip of how to do the sum of any kind of geometric series that converge? I've been researching, but a... |
$$\sum_{n\geq0} ({\frac{2}{3}})^{2n-1}$$
I managed to find that this is a geometric series with common ratio of $4/9$, therefore convergent. That means it's possible to calculate the sum of the series. Can I get any tip of how to do the sum of any kind of geometric series that converge? I've been researching, but al... |
Suppose $R=S/I$ is the homomorphic image of a local Cohen-Macaulay ring $(S,m)$.
I know the completion of $R$ as an $S$-module is just
$R \otimes \hat S$, where $\hat S$ is the $m$-adic completion of $S$.
Is this also the completion of $R$ as a ring?
(I think this comes down to showing that the inverse limit of $S/... |
There is a 5 by 5 matrix of points on a plane. How many triangles can be formed using points on this matrix? |
There is a 5 by 5 matrix of points on a plane. How many triangles can be formed using points on this matrix? |
I've recently come upon the following (seemingly) simple observation:
**Claim**: A positive integer $k = d d^{\prime} > 1$ has the opposite parity of $\text{gcd}(d+1,d^{\prime}+1)$ for any pair of distinct divisors $d$ and $d^{\prime}$ of $k$.
I'm sure there is a simpler proof, but the shortest seems to follow fr... |
I don't have an answer for the applications (so feel free to vote me down, I guess?), but the proof is much simpler conceptually if you do it in cases:
Let $k = ab$, and if a is odd and b is even, then the product is even and the divisors swap parity when you add one, so they don't have a factor of two in common. If... |
I've recently come upon the following (seemingly) simple observation:
**Claim**: A positive integer $k = d d^{\prime} > 1$ has the opposite parity of $\text{gcd}(d+1,d^{\prime}+1)$ for any pair of distinct divisors $d$ and $d^{\prime}$ of $k$.
There are substantially simpler proofs (see comments), but one follows... |
The definition of a Cumulative Distribution Function $(CDF)$ says that
$$P(X \le x) = F(x)$$
This is all good.
Then my text book gives the following theorem without proof:
$$P(X \lt x) = F(x-)$$
The book says that the proof is easy, but with my rusted calculus skills, I have trouble to even intuitively under... |
The definition of a Cumulative Distribution Function $(CDF)$ says that
$$P(X \le x) = F(x)$$
This is all good.
Then my text book gives the following theorem without proof:
$$P(X \lt x) = F(x-)$$
The book says that the proof is easy, but with my rusted calculus skills, I have trouble to even intuitively under... |
I don't have an answer for the applications question (so feel free to vote me down, I guess?), but the proof is much simpler conceptually if you do it in cases:
Let $k = ab$, and if a is odd and b is even, then the product is even and the divisors swap parity when you add one, so they don't have a factor of two in c... |
I've recently come upon the following (seemingly) simple observation:
**Claim**: A positive integer $k = d d^{\prime} > 1$ has the opposite parity of $\text{gcd}(d+1,d^{\prime}+1)$ for any pair of distinct divisors $d$ and $d^{\prime}$ of $k$.
There are substantially simpler proofs (see comments), and one follows... |
I am interested in a system of differential equations that is non-linear, but it doesn't seem to be too crazy. I'm not very good at non-linear stuff, so I thought I'd throw it out there.
The actual equations I'm looking at have several parameters that'd I'd like to tweak eventually.
q' = k - m / r
r' = i... |
I've recently come upon the following (seemingly) simple observation:
**Claim**: A positive integer $k = d d^{\prime} > 1$ has the opposite parity of $\text{gcd}(d+1,d^{\prime}+1)$ for any pair of distinct divisors $d$ and $d^{\prime}$ of $k$.
There are substantially simple proofs (see comments), and one proof fo... |
If I have a stochastic matrix X- the sum of each row is equal to 1 and all elements are non-negative.
Given this property, how can I show that:
x'X=x', x>=0
Has a non-zero solution?
I'm assuming this has something to do with proving a feasible dual, but not may be wrong.. |
I'm trying to use inverse cosine, in the cosine rule to find an angle of a triange when you know 3 sides. I know this formula and have it written down. However I've left my calculator and I'm having to use Google:
http://www.google.co.uk/webhp?hl=en#sclient=psy&hl=en&site=webhp&source=hp&q=arccos((5.9%5E2+%2B+4.1%5E... |
One way to solve this problem is to expand in terms of a power series as follows:
First notice that
$x^x = e^{\ln(x) x} = \sum_{n=0}^\infty \frac{(\ln(x) x)^n}{n!} $
Integrating on both sides from $1$ to $10$ gives
$\int_1^{10} x^x dx = \sum_{n=0}^\infty \frac{1}{n!} \int_1^{10} x^n \ln(x)^n dx $
The fun... |
I've recently come upon the following (seemingly) simple observation:
**Claim**: A positive integer $k = d d^{\prime} > 1$ has the opposite parity of $\text{gcd}(d+1,d^{\prime}+1)$ for any pair of distinct divisors $d$ and $d^{\prime}$ of $k$.
There are substantially simple proofs (see comments), and one proof fo... |
So suppose I want a path from 0 to $c>0$ on the real line, and I am going to use the function $S(t)$ to get there in (discrete) time $T$. That is, my position at time 0 is 0, my position at time $T$ is $c$, and my position $P_t$ changes in the following way:
$$
P_t = (1-\gamma) P_{t-1} + \gamma S(t)
$$
where $\... |
How many digits are required to write the natural numbers from 1 to n, where n is a k-digit number?
|
Start with the one digit numbers. How many digits are needed for them. Do you include zero? How many digits to go from 10 through 99? And so on... |
This is the obvious approach (to me, at least), and is mostly a matter of bookkeeping. To begin with, there are ${{5^2} \choose 3}$ sets of three points. However, some of these are colinear, which we don't want to count.
There are $2 \times 5 \times {5 \choose 3}$ horizontal or vertical sets of three colinear poin... |
How to transform a second degree differential equation into two first degree linear equations? |
Forgive the total beginner question, it's been a few years since I needed to do this stuff.
What is the simplification of (1 + x)^n? |
Forgive the total beginner question, it's been a few years since I needed to do this stuff.
What is the expansion of (1 + x)^n?
Edit: substituted expansion for simplification. |
What is an example of a second order differential equation for which it is known that there are no smooth solutions? |
I have the following formula:
![Formula][1]
This essentially boils down to:
![alt text][2]
I have to check whether this applies to certain universes. But my result depends on whether I can assume that x can also equal y, because in that case the condition will never be true (how could a number be smaller than a... |
Predicate logic: Two variables - same value allowed? |
I have the following formula:
$\exists y \forall x ((x \geq y) \wedge \neg(y \geq x))$
This essentially boils down to:
$\exists y \forall x (x > y)$
I have to check whether this applies to certain universes. But my result depends on whether I can assume that x can also equal y, because in that case the conditio... |
I would like to understand why polynomial multiplication works the way it is defined. For example, we know that $(x+1)^2 = x^2+2x+2$, but how can we prove that this actually works?
More generally, how did we came up with the method used to multiply polynomials?
Any insight would be appreciated. |
I would like to understand why polynomial multiplication works the way it is defined. For example, we know that $(x+1)^2 = x^2+2x+1$, but how can we prove that this actually works?
More generally, how did we came up with the method used to multiply polynomials?
Any insight would be appreciated. |
Is category theory worth learning for the sake of learning it? Can it be used in applied mathematics/probability? I am currently perusing *Categories for the Working Mathematician* by Maclane. |
What are the prerequisites for learning category theory? |
A group $G$ is is *abelian* if
$$ ab = ba $$
for all pairs of elements $a,b \in G$, i.e., if multiplication commutes. Another way of stating this condition is that the *identity map* $\mathrm{id}$ gives an isomorphism between left- and right- multiplication. In other words, we can think of left-and right- multi... |
Can nonabelian groups still have isomorphic left- and right- multiplication? |
Is category theory worth learning for the sake of learning it? Can it be used in applied mathematics/probability? I am currently perusing *Categories for the Working Mathematician* by Mac Lane. |
Let 'f' be a continous but nowhere differentiable function. Is f convolved with mollifier, a smooth function ? |
Let 'f' be a continous but nowhere differentiable function. Is 'f' convolved with mollifier, a smooth function ? |
Let '$f$' be a continous but nowhere differentiable function. Is $f$ convolved with mollifier, a smooth function ? |
A group $G$ is is *abelian* if
$$ ab = ba $$
for all pairs of elements $a,b \in G$, i.e., if multiplication commutes. Another way of stating this condition is that the *identity map* $\mathrm{id}$ gives an isomorphism between left- and right- multiplication. In other words, we can think of left-and right- multi... |
Note that $L$ is a one-to-one homomorphism from $G$ to $S_G$, while $R$ is a one-to-one homomorphism from $G^{\mathrm{op}}$ to $S_G$ ($R(ab) = R(b)\circ R(a)$, so you have an anti-homomorphism if you work with $G$).
You could ask more generally if these two subgroups of $S_G$ are conjugate. That is, do there exist p... |
It makes sense to consider some sets of combinatorial objects as spaces (or [polytopes][1]) and therefore discuss dimensionality (e.g. the set of n by n (-1,0,+1)-matrices). Although, perhaps the word "dimension" could better be described as "[degrees of freedom][2]".
> Mathematically, degrees of freedom is
> the ... |
A divisor $d$ of $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}}$ is _unitary_ if and only if $d = p_{1}^{\varepsilon_{1}} \cdots p_{n}^{\varepsilon_{n}}$, where each exponent $\varepsilon_{i}$ is either $0$ or $r_{i}$. Let $D_{k} = ${ $d$ } be the subset of unitary divisors of an integer $k > 1$ satisfying $\omega(d) = \omega... |
A divisor $d$ of $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}}$ is _unitary_ if and only if $d = p_{1}^{\varepsilon_{1}} \cdots p_{n}^{\varepsilon_{n}}$, where each exponent $\varepsilon_{i}$ is either $0$ or $r_{i}$. Let $D_{k} = ${ $d$ } be the subset of unitary divisors of an integer $k > 1$ satisfying $\omega(d) = \omega... |
A divisor $d$ of $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}}$ is _unitary_ if and only if $d = p_{1}^{\varepsilon_{1}} \cdots p_{n}^{\varepsilon_{n}}$, where each exponent $\varepsilon_{i}$ is either $0$ or $r_{i}$. Let $D_{k} = ${ $d$ } be the subset of unitary divisors of an integer $k > 1$ satisfying $\omega(d) = \omega... |
How compute the total number of common divisors between two given pairs of integers ?
For example,if we consider `(12,24)` the answer is **6** i.e `{1,12,2,6,3,4}`. |
How compute the total number of common divisors between two given pairs of integers ?
For example,if we consider `(12,24)` the answer is **6** i.e `{1,12,2,6,3,4}`.
EDIT : I got an answer [here][1].
[1]: http://books.google.co.in/books?id=di0WSsXV74wC&pg=PA8&lpg=PA8&dq=%22Number+of+common+divisors%22&sour... |
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