On Lebesgue–Ramanujan–Nagell Type Equations

Sharma, Richa

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

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2021

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Cited by 2 publications

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“…In particular, there are many interesting results about the integer solutions of this equation for d = 1 and we direct the reader to the papers [2,7,13,16,17] for more information. For a survey on this very interesting subject we recommend [15,19]. On the other hand (1.1) for square-free d and odd m was well investigated under the conditions gcd(x, y) = 1 and gcd(n, 2h(−cd)) = 1, where h(∆) denotes the class number of Q( √ ∆).…”

Section: Introductionmentioning

confidence: 99%

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On the Diophantine Equation $$cx^2+p^{2m}=4y^n$$

Chakraborty

Hoque²,

Kotyada

2021

Results Math

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We investigate the solvability of the Diophantine equation in the title, where d > 1 is a square-free integer, p, q are distinct odd primes and x, y, a, b are unknown positive integers with gcd(x, y) = 1. We describe all the integer solutions of this equation, and then use the main finding to deduce some results concerning the integers solutions of some of its variants. The methods adopted here are elementary in nature and are primarily based on the existence of the primitive divisors of certain Lehmer numbers.

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Section: Introductionmentioning

confidence: 99%

“…Let d ∈ {2, 3, 7, 11, 19, 43, 67, 163} and p > 41 be a prime. Then (d + p) p ≡ d (mod p) and we have: 3,7,11,19,43, 67, 163} and p > 41 be a prime such that d + p is also a prime. Then the Diophantine equation 11,15,19,35,39,43,51,55,67,91,95,111,115,123,155,163,183,187,195,203…”

Section: Introductionmentioning

confidence: 99%