I was looking at this website: http://mathworld.wolfram.com/LegendreSymbol.html which had a simple overview of Legendre Symbols and the Law of Quadratic Reciprocity. but I saw one thing that surprised me. We all know that the Legendre Symbol has a value of 1 or -1, depending if a is a quadratic residue modular some prime p. This website also defined the Legendre Symbol as taking a value of 0 if p divides a. We all know this as just saying you can't find the Legendre symbol if p divides a. I thought it was interesting that somebody would view this as having a value 0.

Another Value for a Legendre Symbol?