On a Theorem of Tartakowsky

Abstract

Binomial Thue equations of the shape Aan − Bbn = 1 possess, for A and B positive integers and n ≥ 3, at most a single solution in positive integers a and b. In case n ≥ 4 is even and A = 1, an old result of Tartakowsky characterizes this solution, should it exist, in terms of the fundamental unit in Q( √ B). In this note, we extend this to certain values of… (More)

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