Hi everyone! I have a problem in solving my number theory homework. My question is as follows:
If $n$ is a positive integer and if an integer $x$ exists such that $x^{n-1}= 1 mod n$ and $x^{\frac{n-1}{q}} =/= 1 \mod n$ for all prime divisors $q$ of $n-1$, then $n$ is prime.
Please edit my writing because I cannot install MathJax in my computer. Thank you for any help!
I believe we have to use some reasoning on the order of $x$, but I don't know where to start. Thanks!
PLease let me know why you closed my question? Thanks!
