MathDB

Function on integers

Source: 67 Polish MO 2016 Second Round - Problem 3

April 30, 2018

algebrafunctionPoland

Problem Statement

Determine, whether exists function

f

, which assigns each integer

k

, nonnegative integer

f(k)

and meets the conditions:

f(0) > 0

, for each integer

k

minimal number of the form

f(k - l) + f(l)

, where

l \in \mathbb{Z}

, equals

f(k)