Solution of the Diophantine equation x² + p^k=yⁿ

2024/02/29 by Ghosh, Arkabrata
#11D41 #11D61 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.19445

Abstract

The main aim of this article is to find all solutions of the Diophantine equation x² + p^k=yⁿ where p ≡ 1 \pmod 4, (p-1)/(3) is a perfect square and the class number of ℤ[√(-p)] is 2. In this article, I used a method involving prime factorization and class numbers which is different from using congruent number argument which is widely used in this type of problem.

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