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- W2597593886 abstract "Let (U n ) n≥0 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 $$ {alpha}_1{U}_{n1}+cdots +{alpha}_t{U}_{n1}={b}_1{p}_1^{z_1}+cdots {b}_s{p}_s^{z_s}. $$ 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. Bertók, L. Hajdu, I. Pink, and Z. Rábai, Linear combinations of prime powers in binary recurrence sequences, Int. J. Number Theory, 13(2):261–271, 2017]." @default.
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- W2597593886 date "2017-10-01" @default.
- W2597593886 modified "2023-09-26" @default.
- W2597593886 title "Linear combinations of prime powers in sums of terms of binary recurrence sequences" @default.
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- W2597593886 doi "https://doi.org/10.1007/s10986-017-9374-z" @default.
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