• ASIM PATRA

      Articles written in Proceedings – Mathematical Sciences

    • Exact divisibility by powers of the Pell and Associated Pell numbers

      G K PANDA ASIM PATRA

      More Details Abstract Fulltext PDF

      Let $P_n$ be the $n$-th Pell number and $Q_n$ be the $n$-th Associated Pell number. We obtain certain divisibility and exact divisibility results for the powers of the Pell and Associated Pell numbers by applying the concept of $p$-adic valuation of the numbers. In particular, we show that $P^k_n\mid\mid m$ if and only if $P^{k+1}_n\mid\mid P_{nm}$ for all $m, n \geq 2$ and $k \geq 1$. In addition, $Q^k_n\mid\mid m$ if and only if $Q^{k+1}_n\mid\mid Q_{nm}$ for all $m, n \geq 2$ and $k \geq 1$ is also proved.

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