Determine which primes > 3 divide some number of the form 3n^2 - 5n + 1 and which do not.
Not only the above tells you what primes divide the quadratic in n but it also tells you how to find the n's!
For example, take it must be that is a square modulo 13, but:
we've a solution for each n s.t. , and choosing n=3 we indeed get
And with and etc.