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Floor and Ceiling

Source: Austrian Federal Competition 2013, part 2, problem 1

June 18, 2013
floor functionceiling functioninequalitiesalgebra proposedalgebra

Problem Statement

For each pair (a,b)(a,b) of positive integers, determine all non-negative integers nn such that b+⌊na⌋=⌈n+ba⌉.b+\left\lfloor{\frac{n}{a}}\right\rfloor=\left\lceil{\frac{n+b}{a}}\right\rceil.
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