Proof by Contradiction || Prove that an equation can never be a square number

[haxan7]

Homework Statement

Prove that for any integer n n^2+n+1, can never be a square number.

Homework Equations

None.

The Attempt at a Solution

We could put the equation to a^2, (where a^2 is a square number) and solve for n and show that n can not be an integer.
I tried quadratic formula on the equation but the solution gets too messy, and i can't prove that the answer is not an integer.
There must be an easier way to solve this. Just point me in the right direction.

 

[gabbagabbahey]

Homework Statement

Prove that for any integer n n^2+n+1, can never be a square number.

That's going to be very hard to prove, as it isn't true: (-1)²+(-1)+1=1=(1)^2

 

[haxan7]

That's going to be very hard to prove, as it isn't true: (-1)²+(-1)+1=1=(1)^2

Sorry, the question was "for any positive integer n", how do i edit the thread?

 

[tainted]

There should just be a button that says edit in the bottom right of your post.

 

[haxan7]

There should just be a button that says edit in the bottom right of your post.

You can't edit your posts after 700 minutes.

 

[haxan7]

Problem Solved, close this thread.