Vol. 72, No. 2, 1977

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Determination of a unique solution of the quadratic partition for primes p 1 (mod 7)

Budh Singh Nashier and A. R. Rajwade

Vol. 72 (1977), No. 2, 513–521
Abstract

Let p be a rational prime 1 (mod 7). Williams shows that a certain triple of a Diophantine system of quadratic equations has exactly six nontrivial solutions. We obtain here a congruence condition which uniquely fixes one of these six solutions. Further if 2 is not a seventh power residue (mod p) then we obtain a congruence (mod p) for 2(p1)7 in terms of the above uniquely fixed solution.

Mathematical Subject Classification
Primary: 10B05, 10B05
Milestones
Received: 4 April 1977
Published: 1 October 1977
Authors
Budh Singh Nashier
A. R. Rajwade