5

Part of 1995 Turkey MO (2nd round)

Problems(1)

Turkish MO 1995 P5

Source: Turkish Mathematical Olympiad 2nd Round 1995

t(A)

denote the sum of elements of a nonempty set

A

of integers, and define

t(\emptyset)=0

X

of positive integers such that for every integers

k

there is a unique ordered pair of disjoint subsets

(A_{k},B_{k})

X

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

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