If 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))?

Re: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n

Quote:

Originally Posted by

**ehpoc** If p and q are distinct primes, find the number of distinct divisors of

.

Any divisor of has the form where

How many does that make?

Re: 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?

Re: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n

Quote:

Originally Posted by

**ehpoc** I am not concerned.

Pray tell what does that mean?

Quote:

Originally Posted by

**ehpoc** 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?

No, that is not correct.

For example, there are **ten** distinct divisors of .

If you read reply #2 carefully it contains the answer to the OP.

Re: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n

Quote:

Originally Posted by

**ehpoc** 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))?

Find the number of distinct divisors of

Re: 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.

Re: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n

Not relatively prime divisor.

Re: 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?

Re: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n

Quote:

Originally Posted by

**ehpoc** so (p^m)(q^n) has mn many divisors?

There are m + 1 integers between 0 to m and n + 1 integers between 0 and n.

Re: 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)?

Re: If p and q are distinct primes, find the number of distinct divisors of (p^m)(q^n