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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Abstract	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.
AbstractList	We describe a computationally efficient approach to resolving equations of the form C1x2+C2=yn in coprime integers, for fixed values of C1, C2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier. We describe a computationally efficient approach to resolving equations of the form $$C_1x^2 + C_2 = y^n$$ C 1 x 2 + C 2 = y n in coprime integers, for fixed values of $$C_1$$ C 1 , $$C_2$$ C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier. 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.
Author	Patel, Vandita
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Snippet	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... We describe a computationally efficient approach to resolving equations of the form $$C_1x^2 + C_2 = y^n$$ C 1 x 2 + C 2 = y n in coprime integers, for fixed... We describe a computationally efficient approach to resolving equations of the form C1x2+C2=yn in coprime integers, for fixed values of C1, C2 subject to...
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SubjectTerms	Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematical analysis Mathematics Mathematics and Statistics Number Theory
Title	A Lucas–Lehmer approach to generalised Lebesgue–Ramanujan–Nagell equations
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