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Ceiling in FE

Source: BdMO 2024 Higher Secondary National P7

March 18, 2024
functional equationceiling functionnumber theoryalgebra

Problem Statement

Find all functions f:N→Nf:\mathbb{N} \to \mathbb{N} such thatf(⌈f(m)n⌉)=⌈mf(n)⌉f\left(\Big \lceil \frac{f(m)}{n} \Big \rceil\right)=\Big \lceil \frac{m}{f(n)} \Big \rceilfor all m,n∈Nm,n \in \mathbb{N}.
Proposed by Md. Ashraful Islam Fahim
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