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x_n+x_{k}=x_{nk}, strictly increasing with terms naturals

Source: 1987 Greece MO Grade XII p3

September 6, 2024
algebraSequencerecurrence relation

Problem Statement

There is no sequence xnx_n strictly increasing with terms natural numbers such that : xn+xk=xnk,  for any   n,k∈N∗ x_n+x_{k}=x_{nk}, \ \ for \, any \,\,\, n, k \in \mathbb{N}^*
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