1. The problem statement, all variables and given/known data We have JUST started writing proofs recently, and I am a little bit doubtful in my abilities in doing this, so I just want to verify that my proof actually works. I was expecting this one to be a lot longer since the previous 2 were. I don't see any glaring flaws in it, but I'd just like to be sure (writing these feel awkward since this is my first proof base course): A necessary condition for an integer to be divisible by 6 is that it is divisible by 2. 2. Relevant equations 3. The attempt at a solution Assume true. Pf./ [For all integers n, if n is divisible by 6, then n is divisible by 2]. Assume 6|n, n ∈ ℤ. By definition, n = 6k, k ∈ ℤ. Consider that n = 2(3k). See that 3k ∈ ℤ has closure by multiplication of the set of integers, and let 3k = t, t ∈ ℤ. Notice n is even since n = (3k) = 2t. Therefore, 2|n. QED.