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.