MathDB

Turkish MO 1995 P5

Source: Turkish Mathematical Olympiad 2nd Round 1995

September 30, 2006

inductioncombinatorics unsolvedcombinatorics

Problem Statement

Let

t(A)

denote the sum of elements of a nonempty set

A

of integers, and define

t(\emptyset)=0

. Find a set

X

of positive integers such that for every integers

k

there is a unique ordered pair of disjoint subsets

(A_{k},B_{k})

X

such that

t(A_{k})-t(B_{k}) = k