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A note on the diophantine equation (a n − 1)(b n − 1) = x 2

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Abstract

Let a, b be fixed positive integers such that a ≠ b, min(a, b) > 1, ν(a−1) and ν(b − 1) have opposite parity, where ν(a − 1) and ν(b − 1) denote the highest powers of 2 dividing a − 1 and b − 1 respectively. In this paper, all positive integer solutions (x, n) of the equation (a n − 1)(b n − 1) = x 2 are determined.

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Authors and Affiliations

  1. Department of Mathematics, Northwest University, Xián, Shaanxi, P. R. China

    Guo Xiaoyan

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  1. Guo Xiaoyan
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Correspondence to Guo Xiaoyan.

Additional information

Communicated by Attila Pethő

This work is supported by the National Natural Science Foundation of P. R. China (No. 11071194).

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Xiaoyan, G. A note on the diophantine equation (a n − 1)(b n − 1) = x 2 . Period Math Hung 66, 87–93 (2013). https://doi.org/10.1007/s10998-012-6964-8

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  • DOI: https://doi.org/10.1007/s10998-012-6964-8

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