MathDB
HMIC loves "quasi"

Source: HMIC 2022/5

April 8, 2022
number theoryF_pfunction

Problem Statement

Let Fp\mathbb{F}_p be the set of integers modulo pp. Call a function f:Fp2→Fpf : \mathbb{F}_p^2 \to \mathbb{F}_p quasiperiodic if there exist a,b∈Fpa,b \in \mathbb{F}_p, not both zero, so that f(x+a,y+b)=f(x,y)f(x + a, y + b) = f(x, y) for all x,y∈Fpx,y \in \mathbb{F}_p. Find the number of functions Fp2→Fp\mathbb{F}_p^2 \to \mathbb{F}_p that can be written as the sum of some number of quasiperiodic functions.
Back to ProblemsView on AoPS