Erdős problem 1136 · problems.science

Does there exist $A\subset \mathbb{N}$ with lower density $>1/3$ such that $a+b\neq 2^k$ for any $a,b\in A$ and $k\geq 0$ ?

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1136.lean

Retained formal statement2 of 4

Müller [Mu11] settled this question in the affirmative: in fact one can take $A$ to be the set of all integers congruent to $3\cdot 2^i\pmod{2^{i+2}}$ for any $i\geq 0$ , which has density $1/2$ .

FormalConjectures/ErdosProblems/1136.leanErdos1136.erdos_1136.variants.mueller1 lineExact file

1Erdos1136.AvoidsPowersOfTwo Erdos1136.muellerSet ∧ Erdos1136.muellerSet.HasDensity (1 / 2)

SolvedStatement only, no proof

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