GREATEST COMMON DIVISOR OF SHIFTED PELL NUMBERS AND BALANCING NUMBERS
DOI:
https://doi.org/10.18173/2354-1059.2026-0029Keywords:
Pell, Pell-Lucas, balancing or Lucas - balancing numbersAbstract
Let $D_n$ denote the $n$'th Pell, Pell -Lucas, Balancing or Lucas - Balancing number and let $k$ be a positive integer. We find necessary and sufficient conditions on $s$ and $t$ so that the function $n\mapsto \gcd(D_n+s, D_{n+k}+t)$ is unbounded. Then, we give some nice applications for Diophantine equations.
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