IMO Shortlist 2014 problem N8


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7. svibnja 2017.
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For every real number x, let \lVert x \rVert denote the distance between x and the nearest integer. Prove that for every pair (a, b) of positive integers there exist an odd prime p and a positive integer k satisfying \left\lVert \frac{a}{p^k} \right\rVert + \
  \left\lVert \frac{b}{p^k} \right\rVert + \
  \left\lVert \frac{a + b}{p^k} \right\rVert = 1 \text{.}

(Hungary)

Izvor: https://www.imo-official.org/problems/IMO2014SL.pdf