# Indirect Proof question

• June 16th 2014, 10:49 PM
Benja303
Indirect Proof question
Using and indirect proof prove that if n is an integer and 5n^2+ 19 is even, then n is
odd.
• June 16th 2014, 11:22 PM
romsek
Re: Indirect Proof question
Quote:

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.
• June 21st 2014, 04:29 AM
HallsofIvy
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.