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Sequence of positive integers

Source: 1st TASIMO, Day1 Problem2

May 18, 2024
Sequencealgebra

Problem Statement

Find all positive integers (r,s)(r,s) such that there is a non-constant sequence ana_n os positive integers such that for all n=1,2,…n=1,2,\dots an+2=(1+a2ra1s)(1+a3ra2s)…(1+an+1rans). a_{n+2}= \left(1+\frac{{a_2}^r}{{a_1}^s} \right ) \left(1+\frac{{a_3}^r}{{a_2}^s} \right ) \dots \left(1+\frac{{a_{n+1}}^r}{{a_n}^s} \right ). Proposed by Navid Safaei, Iran
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