Equations in prime powers

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

Vol. 118 (1985), No. 2, 359–367

DOI: 10.2140/pjm.1985.118.359

Abstract

Equations of form p^a = (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