MathDB

Interesting NT function

Source: Indonesia TSTST - Number Theory

February 29, 2024

functionnumber theoryIndonesiaIndonesia TSTcomplete residue systemresidueFE NT

Problem Statement

Find all functions

f:\mathbb{N} \rightarrow \mathbb{N}

such that for every prime number

p

and natural number

x

\{ x,f(x),\cdots f^{p-1}(x) \}

is a complete residue system modulo

p

. With

f^{k+1}(x)=f(f^k(x))

for every natural number

k

and

f^1(x)=f(x)

.
Proposed by IndoMathXdZ