Vol. 101, No. 2, 1982

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Exponential Diophantine equations

J. L. Brenner and Lorraine L. Foster

Vol. 101 (1982), No. 2, 263–301
Abstract

We study equations in which the unknowns are the exponents. (Work in this field originated with C. Størmer and D. H. Lehmer. More recently, Leo J. Alex has extended their results; his work relates to classification of nonabelian simple groups.)

  • For the equation k + 7α = 3c + 5d, k = 3b,5b,13b, or 17b, and for many similar 4-term equations, we find all integral solutions.
  • We find all integral solutions of 3α + 7b = 3c + 5d + 2.
  • We prove that there are infinitely many odd m such that mα+7b = 3c+5d has only the solutions (a,b,c,d) = (0,0,0,0),(0,1,1,1).

Mathematical Subject Classification
Primary: 10B25, 10B25
Milestones
Received: 6 November 1980
Published: 1 August 1982
Authors
J. L. Brenner
Lorraine L. Foster