Erdős Problems

1,217 source-owned questions · 604 with a formal statement · searchable by statement, number, topic and source status.

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5 Problems

Number	Question	Source says	Formal	Result here
#124	Let $3\leq d_1 < d_2 < \cdots < d_r$ be integers such that all sufficiently large integers can be written as a sum of the shape $\sum_i c_ia_i$ where $c_i \in \{0, 1\}$ and $a_i$ has only the digits $0, 1$ when written in base $d_i$ . Then $\sum_{1 \le i \le r}\frac 1{d_i - 1} \ge 1.$ Source says openFormalized	open	In Lean	No Result decision
#125	Case 3: Does $A + B$ have positive upper and lower density that are equal? This is the literal interpretation of "positive density" which was falsified.Source says disproved (Lean)Formalized	disproved (Lean)	In Lean	No Result decision
#376	Are there infinitely many $n$ such that ${2n\choose n}$ is coprime to $105$ ?Source says openFormalized	open	In Lean	No Result decision
#406	Is it true that there are only finitely many powers of $2$ which have only the digits $0$ and $1$ when written in base $3$ ?Source says openFormalized	open	In Lean	No Result decision
#730	Are there infinitely many pairs of integers $n < m$ such that $\binom{2n}{n}$ and $\binom{2m}{m}$ have the same set of prime divisors?Source says openFormalized	open	In Lean	No Result decision