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 :)

Please show us what working you have done towards this question. As it stands, this looks very much like a homework question and people here don't take too kindly to being asked to solve homework problems for users — lioness99a, May 28 '19 at 12:48
Well it's always divisible by $2$ so you just need to check if it's divisible by $11$. If nothing else, you can check the $11$ cases. — saulspatz, May 28 '19 at 12:49
This is practice question, we have learned this for the first time and I go to the practice book and stucked with this one — Or Yehuda Ben Shimol, May 28 '19 at 12:51
@parcly taxel in the original they were not, just wanted to make sure the OP agrees with the new version... (Seems like this version must be correct given the problem as listed, but just to make sure) — abiessu, May 28 '19 at 12:55

score 2 · Answer 1 · answered May 28 '19 at 12:53

2

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 $9\mod11$.

answered May 28 '19 at 12:53

auscrypt

1 Answers1