A Lucas–Lehmer approach to generalised Lebesgue–Ramanujan–Nagell equations

We describe a computationally efficient approach to resolving equations of the form C 1 x 2 + C 2 = y n in coprime integers, for fixed values of C 1 , C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.

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Vydané v:	The Ramanujan journal Ročník 56; číslo 2; s. 585 - 596
Hlavný autor:	Patel, Vandita
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.11.2021 Springer Nature B.V
Predmet:	Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematical analysis Mathematics Mathematics and Statistics Number Theory Lehmer sequences 11D59 Secondary 11D41 Primitive divisor theorem Thue equation Primary 11D61 Exponential equation
ISSN:	1382-4090, 1572-9303
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Popis
Shrnutí:	We describe a computationally efficient approach to resolving equations of the form C 1 x 2 + C 2 = y n in coprime integers, for fixed values of C 1 , C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1382-4090 1572-9303
DOI:	10.1007/s11139-021-00408-9