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arXiv · 1606.01594

Suites r\'ecurrentes lin\'eaires d'ordre 2 \`a divisibilit\'e forte

A. Bauval
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Abstract

We reprove twice, in a simpler but as elementary way, a result by Hor\'ak and Skula (1985) who determined, among all sequences of integers defined by $$u_1=1,\quad u_2=R,\quad u_{n+2}=Pu_{n+1}-Qu_n$$ for some integers $P,Q,R$, those which satisfy the strong divisibility condition $$\forall i,j\in\mathbb N^*\quad u_i\land u_j=\left|u_{i\land j}\right|,$$ where $\land$ denotes the greatest common divisor.

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A. Bauval. 2016-06-06. Suites r\'ecurrentes lin\'eaires d'ordre 2 \`a divisibilit\'e forte. https://arxiv.org/abs/1606.01594

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