Linear combinations of prime powers in sums of terms of binary recurrence sequences

作     者：Meher, Nabin Kumar Rout, Sudhansu Sekhar 

作者机构：Harish Chandra Res Inst HBNI Chhatnag Rd Jhunsi 211019 India 

出 版 物：《LITHUANIAN MATHEMATICAL JOURNAL》 (Lithuanian Math. J.)

年 卷 期：2017年第57卷第4期

页      面：506-520页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：linear recurrence sequence Diophantine equations linear forms in logarithms reduction method 

摘      要：Let (U (n) ) (n0) be a nondegenerate binary recurrence sequence with positive discriminant. Let p (1) , . . . , p (s) be fixed prime numbers, b (1) , . . . , b (s) be fixed nonnegative integers, and a (1) , . . . , a (t) be positive integers. In this paper, under certain assumptions, we obtain a finiteness result for the solution of the Diophantine equation Moreover, we explicitly solve the equation F (n1) + F (n2) = 2 (z1) + 3 (z2) in nonnegative integers n (1), n (2), z (1), z (2) with z (2) z (1). The main tools used in this work are the lower bound for linear forms in logarithms and the Baker-Davenport reduction method. This work generalizes the recent papers [E. Mazumdar and S.S. Rout, Prime powers in sums of terms of binary recurrence sequences, arXiv:1610.02774] and [C. Bertk, L. Hajdu, I. Pink, and Z. Rabai, Linear combinations of prime powers in binary recurrence sequences, Int. J. Number Theory, 13(2):261-271, 2017].