If p and q are distinct primes, find the number of distinct divisors of pmqn.

Would the answer just be

(p^m-m^(m-1))(q^n-q^(n-1))?

- Dec 19th 2011, 06:32 AMehpocIf p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n).
If p and q are distinct primes, find the number of distinct divisors of pmqn.

Would the answer just be

(p^m-m^(m-1))(q^n-q^(n-1))? - Dec 19th 2011, 06:44 AMPlatoRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
- Dec 19th 2011, 07:06 AMehpocRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
I am not concerned. Let me rephrase the question.

I was told the formula for the number of distinct divisors of p^k is p^k-p^(k-1). Is this the correct formula? - Dec 19th 2011, 07:20 AMPlatoRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
- Dec 19th 2011, 08:13 AMAlso sprach ZarathustraRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
- Dec 19th 2011, 08:31 AMehpocRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
Ok I think I know where I went wrong. I got the total number of relatively prime numbers to (p^m)(q^n)

(p^m)(q^n)-(p^m-m^(m-1))(q^n-q^(n-1))

Amount of numbers from 1 to (p^m)(q^n) subtract the amount of numbers that are relatively prime. - Dec 19th 2011, 08:41 AMemakarovRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
Not relatively prime $\displaystyle \not\!\!\!\!\implies$ divisor.

- Dec 19th 2011, 09:00 AMehpocRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
Ya I was never thinking about this question properly.

ok so the number of distinct divisors of p and q are 2 each if they are prime right? p and 1, and q and 1 respectively

So the number of distinct divisors of p^k is k+1?

2^3 has four distinct divisors 4 right? 1, 2, 2^2, 2^3

so (p^m)(q^n) has mn many divisors? - Dec 19th 2011, 09:04 AMemakarovRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
- Dec 19th 2011, 09:32 AMehpocRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
Sorry I kind of made a typo (I am becoming infamous for it unfortunately LOL)

(m+1)(n+1) many distinct divisors of (p^m)(q^n)? - Dec 19th 2011, 09:34 AMemakarovRe: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n
Yes.