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## Homework Statement

Assume n = p_1*p_2*p_3*...*p_r = q_1*q_2*q_3*...*q_s, where the p's and q's are primes. We can assume that none of the p's are equal to any of the q's. Why?

## Homework Equations

## The Attempt at a Solution

I am completely stuck on this. My understanding of the Fundamental Theorem of Arithmetic is that each number n[itex]\geq[/itex]2 has a unique prime factorization. So how could we possibly assume that the p's aren't equal to the q's?