# Math Help - Indirect Proof question

1. ## Indirect Proof question

Using and indirect proof prove that if n is an integer and 5n^2+ 19 is even, then n is
odd.

2. ## Re: Indirect Proof question

Originally Posted by Benja303
Using and indirect proof prove that if n is an integer and 5n^2+ 19 is even, then n is
odd.
Suppose n were even.

$5 n^2 + 19=5(2k)^2+19=20k^2+19$

$20 k^2 + 19$ is clearly odd for any k and thus by contradiction n must be odd.

3. ## Re: Indirect Proof question

A little more detail: Suppose n were even. Then n= 2k for some integer k. $5n^2+ 19= 5(2k)^2+ 19= 5(4k^2)+ 19= 20k^2+ 19= 20k^2+ 18+ 1= 2(10k^2+ 9)+ 1$. Since $5n^2+ 19$ is equal to 2 times an integer plus one, it is odd, not even, a contradiction.