Newsgroups: sci.math
From: shallit@graceland.uwaterloo.ca (Jeffrey Shallit)
Subject: proof of quadratic reciprocity theorem
Date: Mon, 31 Aug 1992 20:01:21 GMT

Jerry Tunnell once showed me the following neat proof of the
quadratic reciprocity theorem.   It goes as follows:

	Let p and q be distinct odd primes.

	(a) p is a square (mod q)

	(b) left multiplication by p gives an even permutation of Z/(q)

	(c) the discriminant of X^q - 1 is a square in Z/(p).

	(d) ((-1)^(q-1)/2) * q is a square (mod p).

	Then (a) <==> (b) <==> (c) <==> (d).

Anybody know who this is originally due to?  Anybody know where
Tunnell is currently?  I couldn't find his address in the
CML.

Jeff Shallit
University of Waterloo