1. The problem statement, all variables and given/known data An integer is called a square-free if it is not divisible by the square of any integer greater than 1: Show that: 2. Relevant equations a is square free if and only if a = (+/-)P1*P2*P3*Pr where Pr are distinct primes. 3. The attempt at a solution So, a is in Z for all b in Z such that b^2 does not divide a and b>1 if and only if a=(+/-)P1P2P3***Pr where Pr are distinct primes Hello, I'm taking a number theory class and the basic proofs are kicking my butt. I understand the concepts but it is very difficult for me to actually prove. For example, my solution I have to state the problem in mathematical equivalents. I don't know if I should make b in Z using the FOR ALL(backwards a) or there exists(mirrored E) for the equation. I want to play with the FTA but I don't know how I can incorporate the a|b into the solution. If and only if means I must go both ways and I'm at a loss. I can see why a must be a product of distinct primes because if p^r and r>=2 then it would be divisible by the square which would not make it square free.