Journal of Integer Sequences, Vol. 25 (2022), Article 22.8.1 |

Department of Mathematics

National University of Mongolia

Baga Toirog

Ulaanbaatar 14200

Mongolia

**Abstract:**

In this paper we obtain a simple formula for the number of matching -ary digits of certain terms of Lucas sequences for any odd prime . Using this formula, we present a simple sufficient condition for the sequence
to be unbounded, where
() are given integers and is the -adic valuation.

Received July 11 2022; revised versions received August 5 2022; August 31 2022; September 13 2022.
Published in *Journal of Integer Sequences*,
October 7 2022.

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