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a_1 <= a_2 <= ..., exists r : r/ a_r= k + 1 => exists t : t/ a_t = k

Source: Dutch BxMO/EGMO TST 2015 p2

August 24, 2019
Integer sequenceSequencealgebranumber theory

Problem Statement

Given are positive integers rr and kk and an infi nite sequence of positive integers a1≤a2≤...a_1 \le a_2 \le ... such that rar=k+1\frac{r}{a_r}= k + 1. Prove that there is a tt satisfying tat=k\frac{t}{a_t}=k.
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