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arXiv · 2610.00119

Some Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k)

Xiaodong Zhuang·Nikos E. Mastorakis
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Abstract

The solution of the Diophantine equation ay^2=b(x^k-c^k) is studied in different cases of k. Methods are proposed for different cases of k, which are convenient for computer algorithm implementation. The original equation is reduced to lower-degree equations, which can improve the efficiency in searching possible integer solutions. A sufficient condition of the unsolvability of ay^2=b(x^2n-c^2n) is presented.

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Xiaodong Zhuang, Nikos E. Mastorakis. 2026-09-09. Some Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k). https://arxiv.org/abs/2610.00119

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