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Odd number generates all the integers

Source: Science ON 2021 grade VII/1

March 8, 2021
Setsnumber theory

Problem Statement

Supoose AA is a set of integers which contains all integers that can be written as 2a−2b2^a-2^b, a,b∈Z≥1a,b\in \mathbb{Z}_{\ge 1} and also has the property that a+b∈Aa+b\in A whenever a,b∈Aa,b\in A. Prove that if AA contains at least an odd number, then A=ZA=\mathbb{Z}.
(Andrei Bâra)
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