Thread: Proof help

Prove that if u is an odd integer, then the equation x^2 + x - u=0 has no solution that is an integer.


You can do this one of two ways, proof by contra positive, or proof by contradiction. I am a little confused on how I want to approach this.

If anyone has any insight, I would be more than appreciative. Thanks in advance.

If x is even then $\displaystyle x^2+x-u$ is odd.

If x is odd then $\displaystyle x^2+x-u$ is also odd.

So it can't be zero.