Erdős problem 361

Let $c > 0$ and $n$ be some large integer. What is the size of the largest set $A \subseteq \{1, \ldots, \lfloor c n \rfloor\}$ such that $n$ is not a sum of a subset of $A$ ? Does this depend on $n$ in an irregular way?

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

361.lean

Retained formal statement3 of 3

For target $4$ and universe $\{1, 2, 3\}$ , the maximum is $2$ : the full set is invalid because its subset $\{1, 3\}$ sums to $4$ .

FormalConjectures/ErdosProblems/361.leanErdos361.maxSubsetSumAvoidingCard_three_four1 lineExact file

1Erdos361.maxSubsetSumAvoidingCard 3 4 = 2

TestStatement only, no proof