# What type of proof is this defined as?

## Homework Statement

I have to prove or disprove the following statement.

The product of an integer and its square is even

## Homework Equations

n2*n
n = 2k + 1 (Odd integers)[/B]

## The Attempt at a Solution

I uploaded a photo of my proof. As you can see, I have proved that if n is an odd integer, the product of n squared and n will be odd as well. My question is what type of proof is this? I was thinking it was proof by counterexample but I wasn't sure if the correct terminology would be "disproof by counterexample". Or is it a proof by contradiction? Any help is appretiated : )

Mark44
Mentor

## Homework Statement

I have to prove or disprove the following statement.

The product of an integer and its square is even

## Homework Equations

n2*n
n = 2k + 1 (Odd integers)[/B]

## The Attempt at a Solution

View attachment 73597
I uploaded a photo of my proof. As you can see, I have proved that if n is an odd integer, the product of n squared and n will be odd as well. My question is what type of proof is this? I was thinking it was proof by counterexample but I wasn't sure if the correct terminology would be "disproof by counterexample". Or is it a proof by contradiction? Any help is appretiated : )
This is a direct proof. You proved the given statement, so what you did is not a disproof. You can't prove a statement by counterexample. To prove an implication by contradiction, you assume the opposite of the conclusion of the implication, and then show that this causes a contradiction.

BTW, where you show several lines that start with "n * n2 = ", you could just continue the line above using '=' and omit the "n * n2 = " part.

Epond89
Fredrik
Staff Emeritus