an:05972332
Zbl 1253.11005
Jakimczuk, Rafael
Generalized cyclotomic numbers of order 2 and the quadratic reciprocity law
EN
Int. J. Contemp. Math. Sci. 6, No. 13-16, 687-706 (2011).
00286670
2011
j
11A15 11D79
quadratic residues; quadratic reciprocity law; congruences
Let \(p\) be an odd prime number; for positive integers \(n\), the author considers the number of solutions of congruences of the form \(a_1x_1^2 + \ldots + a_nx_n^2 \equiv a \bmod p\). Using Dirichlet's theorem on primes in arithmetic progression he then derives the quadratic reciprocity law from his results. Much simpler proofs along these lines have been obtained recently e.g. by \textit{W. Castryck} [Am. Math. Mon. 115, No. 6, 550--551 (2008; Zbl 1228.11006)].
Franz Lemmermeyer (Jagstzell)
Zbl 1228.11006