MathDB

Miklós Schweitzer 2004, Problem 4

Source: Miklós Schweitzer 2004

July 30, 2016

college contestsMiklos Schweitzerfunction

Problem Statement

Determine all totally multiplicative and non-negative functions

f\colon\mathbb{Z}\rightarrow \mathbb{Z}

with the property that if

a, b\in \mathbb{Z}

and

b\neq 0

, then there exist integers

q

and

r

such that

a-qb+r

and

f(r)<f(b)