MathDB

set finding

Source: Romanian IMO Team Selection Test TST 2002, problem 1

July 4, 2005

inductionnumber theory unsolvednumber theory

Problem Statement

Find all sets

A

and

B

that satisfy the following conditions: a)

A \cup B= \mathbb{Z}

; b) if

x \in A

then

x-1 \in B

; c) if

x,y \in B

then

x+y \in A

. Laurentiu Panaitopol