91Ó°ÊÓ

Use Gauss' lemma to compute each of the Legendre symbols below (that is, in each case obtain the integer \(n\) for which \((a / p)=(-1)^{n}\) ): (a) \((8 / 11)\). (b) \((7 / 13)\). (c) \((5 / 19)\). (d) \((11 / 23)\). (c) \((6 / 31)\).

(a) If the prime \(p>3\), show that \(p\) divides the sum of its quadratic residues. (b) If the prime \(p>5\), show that \(p\) divides the sum of the squares of its quadratic nonresidues.