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

• Published in: The Ramanujan journal Vol. 56; no. 2; pp. 585 - 596
• Main Author: Patel, Vandita
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2021; Springer Nature B.V
• Subjects: 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

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.