A problem in additive number theory.

number-theory additive-combinatorics

For the original problem, there is a counterexample for $n=24$ and $A=\{3,9,11,15,20,21,23\}$.

There are no counterexamples for $n \leq 23$.

For the new problem, there is a counterexample:

$n=29$ and $A=\{4,5,6,9,13,22,28\}$.

There are no counterexamples for $n \leq 28$.

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