Find all the integers $n$ with $22\mid n^2+n-2$

Question

Find all the integers $n$ with $22\mid n^2+n-2$

I have tried gcd but I have no idea how to solve this

Thank you :)

Answer 1

Note that $n^2+n-2$ is really $(n+2)(n-1)$ which is always divisible by $2$, and only by $11$ when $n\equiv1$ or $9\mod11$.