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Is there a set of positive integers ?

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September 9, 2010
number theoryAdditive Number TheoryAdditive combinatoricsIMO Shortlist

Problem Statement

Decide whether there exists a set MM of positive integers satisfying the following conditions:
(i) For any natural number m>1m>1 there exist a,b∈Ma, b \in M such that a+b=m.a+b = m.
(ii) If a,b,c,d∈Ma, b, c, d \in M, a,b,c,d>10a, b, c, d > 10 and a+b=c+da + b = c + d, then a=ca = c or a=d.a = d.
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