Vol. 118, No. 2, 1985

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Equations in prime powers

Dennis Ray Estes, Robert M. Guralnick, Murray M. Schacher and Ernst Gabor Straus

Vol. 118 (1985), No. 2, 359–367
Abstract

Equations of form pa = (qn 1)(q 1) are considered where p is prime, q a prime power, and n 3. These equations occur in group theory and in number theory in an attempt to construct algebraic number fields which are arithmetically equivalent but not isomorphic. Algorithms are sought to determine all solutions when p is fixed.

Mathematical Subject Classification 2000
Primary: 11D41
Secondary: 20D05
Milestones
Received: 15 June 1984
Published: 1 June 1985
Authors
Dennis Ray Estes
Robert M. Guralnick
Department of Mathematics
University of Southern California
3620 S. Vermont Ave
Los Angeles CA 90089-2532
United States
http://rcf.usc.edu/~guralnic
Murray M. Schacher
Ernst Gabor Straus