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Part of 2013 Federal Competition For Advanced Students, Part 2

Problems(1)

Floor and Ceiling

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

6/18/2013
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.
floor functionceiling functioninequalitiesalgebra proposedalgebra