On Lebesgue–Ramanujan–Nagell Type Equations

Richa Sharma ()
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Richa Sharma: Malaviya National Institute of Technology Jaipur

A chapter in Class Groups of Number Fields and Related Topics, 2020, pp 147-161 from Springer

Abstract: Abstract Exponential Diophantine equations are classical and even now it is a very active area of research. One of the most important equations of this type is the so-called Lebesgue–Ramanujan–Nagell type equation, $$x^2 + D^m = \lambda y^n,$$where D and $$\lambda $$ are fixed positive integers, and one is looking for its solutions in positive integers. This is a survey article aimed at reviewing results concerning solvability of this equation in positive integers x, y, m and n for $$\lambda =1, 2,4$$.

Keywords: Lebesgue–Ramanujan–Nagell type equations; Integer solution; Lucas sequences; Primitive divisors; Primary: 11D61; Secondary: 11D41 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-15-1514-9_14

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DOI: 10.1007/978-981-15-1514-9_14

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