Direct Proof With Odd Integers

[smiles988]

Homework Statement

If m is an odd integer and n divides m, then n is an odd integer.

Homework Equations

Odd integers can be written in the form m=2k+1.
Since n divides m, there exists an integer p such that m=np

The Attempt at a Solution

We will assume that m is an odd integer and that n divides m. We will show that n is an odd integer. Since m is an odd integer, there exists an integer k such that m=2k+1. Since n divides m, there exists an integer p such that m=np.

I don't know where to go from here to arrive at n is equal to 2*an integer +1. Do I need to use cases?

 

[ircdan]

so you have m = np and m is odd. you want to show n is odd. so suppose it's even, then look what happens, you should get a contradiction.