For $p\gt2$ a prime, and any $q \in \mathbb{Z^+} $,
Show that $\left(\frac{q(q+1)}{p}\right) =\left(\frac{1+q^{-1}}{p}\right )$ where the terms are legendre terms.
I saw this result as part of a proof, and it was simply assumed, like the result was trivial/obvious.. but I cannot seem to see why this is so.. is it a typo? or can someone please explain/prove why?
Thanks heaps!