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aops compiled \lfloor :)

Source: 2022 IRN TWN Friendly math competition P1

June 23, 2022
number theoryfloor functionIranTaiwan

Problem Statement

Let k⩾2k\geqslant 2 be an integer, and a,ba,b be real numbers. prove that a−ba-b is an integer divisible by kk if and only if for every positive integer nn ⌊an⌋≡⌊bn⌋ (mod k)\lfloor an \rfloor \equiv \lfloor bn \rfloor \ (mod \ k)
Proposed by Navid Safaei
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