A Note on Williams' Proof of Scholz's Biquadratic Reciprocity Law
by
Perlas Cabarrubias-Caranay
University of the Philippines Baguio
Coauthors: Dr. Fidel R. Nemenzo

Let p and q be distinct primes such that p \equiv q \equiv 1 mod 4. In this note, we will correct a gap in K. S. Williams' proof of Scholz's Biquadratic reciprocity Law. A counter-example will be given to show that U and Uu+2Tv are not necessarily relatively prime. Finally, Scholz's reciprocity law will be extended to the case where one prime is equal to 2.

Date received: January 4, 2004