(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that for every integer n, 15|n iff 5|n and 3|n.

I have proven the "if" direction. My question regards the "only if" portion of the proof.

So far I have:

(<--) Suppose 5|n and 3|n. Then there are j,k ∈ Z for which n = 5j and n = 3k.

*above, Z stands for the set of integers

I have found that both (j + k)/8 and (j - k)/2 seem to provide the desired value to show that 15|n, however I am not entirely sure how to show that either of these values is an integer (as is required by the definition of "divides"). I assume I am not proposing a clever enough value (or form) for the divisor. Any advice on this?

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple division proof

**Physics Forums | Science Articles, Homework Help, Discussion**