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arXiv · 2504.14518

On some ternary Diophantine equations of Signature $(p,p,k)$

Armand Noubissie·Alain Togbe
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Abstract

In this paper, we summarize the work on ternary Diophantine equation of the form $Ax^n+By^n=cz^m$, where $m \in \{2,3,n\} $, $n\geqslant 7 $ is a prime. Moreover, we completely solve some particular cases ($A=5^{\alpha}, ~B=64,~ c=3, ~m=2; \quad A=2^{\alpha},~ B=27, ~c \in \{7,13\}, ~m=3$).

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Armand Noubissie, Alain Togbe. 2025-04-20. On some ternary Diophantine equations of Signature $(p,p,k)$. https://arxiv.org/abs/2504.14518

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