Verify that is solvable. Thanks in advance!
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 )
Then, as
Tonio
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 .
Then,
Besides "brute force", how can I find values of p that satisfy the equation ?