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## Homework Statement

prove using induction:

for any n =1,2,3...

the product of the divisors of n = n^(number of divisors of n (counting 1 and n)/2)

## Homework Equations

## The Attempt at a Solution

I understand why this is the case, but I'm having trouble with the induction step.

if the product of the divisors of k = k^(number of divisors of k/2), the the product of the divisors of k+1 = k^(number of divisors of k+1/2). I know that k and k+1 are relatively prime, so all their divisors are different. But I can't seem to make that final connection