Thread: (p^m)(q^n) Distinct Odd Primes

Show that a number of the form (p^m)(q^n), where p and q are Distinct Odd Primes,can never be a perfect number. Also show that a number of the form (3^m)(5^n)(11^k) can never be a perfect number.

Originally Posted by Wachoorou

Show that a number of the form (p^m)(q^n), where p and q are Distinct Odd Primes,can never be a perfect number. Also show that a number of the form (3^m)(5^n)(11^k) can never be a perfect number.

Odd Perfect numbers

We want

but

Clear denominators, see what has to divide what, and figure out the possible values of m and n.

The proof is similar for the second case.