Find the value of $(\frac{1\cdot 2}{73})+(\frac{2\cdot 3}{73})+...+(\frac{71\cdot 72}{73})$.
This is based off each fraction being a Legendre Symbol.
I tried to find a pattern... but I could't find anything. Also, I tried using Euler's Criterion since 73 is prime, but I still didn't see a fast way to figure this out.