The Legendre symbol (a | p) shows whether or not is a quadratic residue modulo p. If it is 1, then a is a quadratic residue modulo p, and if it's -1, then it’s not.
I learned about this in the Open University course M381 – Number theory and mathematical logic and wrote this web page / tool to help show the steps involved in evaluating a Legendre symbol. To see how it was made, either view source or check out the repository on GitHub at smcgivern/legendre-symbol-evaluator.