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arXiv · 1812.11874

Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations

Kalyan Chakraborty·Azizul Hoque·Richa Sharma
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Abstract

It is well-known that for $p=1, 2, 3, 7, 11, 19, 43, 67, 163$, the class number of $\mathbb{Q}(\sqrt{-p})$ is one. We use this fact to determine all the solutions of $x^2+p^m=4y^n$ in non-negative integers $x, y, m$ and $n$.

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Kalyan Chakraborty, Azizul Hoque, Richa Sharma. 2018-12-31. Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations. https://arxiv.org/abs/1812.11874

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