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INAMO 2019 P5

Source: INAMO 2019 P5

July 3, 2019
Inamoalgebra

Problem Statement

Given that aa and bb are real numbers such that for infinitely many positive integers mm and nn, ⌊an+b⌋≥⌊a+bn⌋ \lfloor an + b \rfloor \ge \lfloor a + bn \rfloor ⌊a+bm⌋≥⌊am+b⌋ \lfloor a + bm \rfloor \ge \lfloor am + b \rfloor Prove that a=ba = b.
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