This follows at once from the properties of Legendre's symbol and Gauss' Quadratic Reciprocity Law.
But if you haven't yet studied this or if you can't use it then I know of no methods but "wise" brutal force: for example, it's not too hard to
check that (just taking multiples of 89 and checking which one summed to 5 is a perfect square. In this case it was )
Thank you all so much! My understanding of the Legendre symbol was a little unclear, but not anymore
So if I wanted to show that for what primes p would make solvable, I would set .
Besides "brute force", how can I find values of p that satisfy the equation ?