TY - JOUR
T1 - On the Shorey–Tijdeman Diophantine equation involving terms of Lucas sequences
AU - Ddamulira, Mahadi
AU - Luca, Florian
AU - Tichy, Robert
N1 - Publisher Copyright:
© 2021 The Author(s)
PY - 2022/3
Y1 - 2022/3
N2 - Let r≥1 be an integer and U≔{Un}n≥0 be the Lucas sequence given by U0=0,U1=1, and Un+2=rUn+1+Un for n≥0. In this paper, we explain how to find all the solutions of the Diophantine equation, AUn+BUm=CUn1+DUm1, in integers r≥1, 0≤m11, AUn≠CUn1, where A,B,C,D are given integers with A≠0,B≠0, m,n,m1,n1 are nonnegative integer unknowns and r is also unknown.
AB - Let r≥1 be an integer and U≔{Un}n≥0 be the Lucas sequence given by U0=0,U1=1, and Un+2=rUn+1+Un for n≥0. In this paper, we explain how to find all the solutions of the Diophantine equation, AUn+BUm=CUn1+DUm1, in integers r≥1, 0≤m11, AUn≠CUn1, where A,B,C,D are given integers with A≠0,B≠0, m,n,m1,n1 are nonnegative integer unknowns and r is also unknown.
KW - Diophantine equations
KW - Lucas sequences
UR - http://www.scopus.com/inward/record.url?scp=85113802505&partnerID=8YFLogxK
U2 - 10.1016/j.indag.2021.08.001
DO - 10.1016/j.indag.2021.08.001
M3 - Article
AN - SCOPUS:85113802505
VL - 33
SP - 314
EP - 321
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
SN - 0019-3577
IS - 2
ER -