# Prime Factorization (Arithmetic)

## 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?

## The Attempt at a Solution

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

Office_Shredder
Staff Emeritus
Gold Member
2021 Award
Is this literally the statement of your homework question?

phyzguy