olymmath

TSTST 2022 Problem 3

  • Answer

Determine all positive integers NN for which there exists a strictly increasing sequence of positive integers s0<s1<s2<⋯s_{0}<s_{1}<s_{2}<\cdots satisfying the following properties: - the sequence s1−s0,s2−s1,s3−s2,…s_{1}-s_{0}, s_{2}-s_{1}, s_{3}-s_{2}, \ldots is periodic; and - ssn−ssn−1≤N<s1+sn−ssn−1s_{s_{n}}-s_{s_{n-1}} \leq N<s_{1+s_{n}}-s_{s_{n-1}} for all positive integers nn.

Dataset text NuminaMath olympiads. Quoted with source.

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t^{2} \leq N < t^{2} + t

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