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Floor of an AP is always a perfect square

Source: 2023 4th OMpD L2 P2 - Brazil - Olimpíada Matemáticos por Diversão

September 21, 2023
floor functionalgebraBoundingArithmetic Progression

Problem Statement

Find all pairs (a,b)(a,b) of real numbers such that ⌊an+b⌋\lfloor an + b \rfloor is a perfect square, for all positive integer nn.
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