Counterexamples to a Conjecture of Dombi in Additive Number Theory

12/23/2022

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by   Jason P. Bell, et al.

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We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find examples of sets A ⊂ℕ with the property that ℕ∖ A is infinite, but the sequence n → |{ (a,b,c) : n=a+b+c and a,b,c ∈ A }|, counting the number of 3-compositions using elements of A only, is strictly increasing.