MathDB
divisibility functional with primes , f(p) > 0, p| (f(x) + f(p))^{f(p)}- x

Source: Dutch IMO TST2 2019 p4

January 11, 2020
number theoryfunctionFind all functionsprime numbersfunctional equation

Problem Statement

Find all functions f:Z→Zf : Z \to Z satisfying ∙\bullet f(p)>0 f(p) > 0 for all prime numbers pp, ∙\bullet p∣(f(x)+f(p))f(p)−xp| (f(x) + f(p))^{f(p)}- x for all x∈Zx \in Z and all prime numbers pp.
Back to ProblemsView on AoPS