MathDB
Cute division problem

Source: Iran 2024 3rd round P4

August 25, 2024
number theory

Problem Statement

For a given positive integer number nn find all subsets {r0,r1,⋯ ,rn}⊂N\{r_0,r_1,\cdots,r_n\}\subset \mathbb{N} such that
nn+nn−1+⋯+1∣nrn+⋯+nr0. n^n+n^{n-1}+\cdots+1 | n^{r_n}+\cdots+ n^{r_0}.
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