Problem 376

Erdős Problem #376: declared status 'open'. Formalized: yes. Are there infinitely many $n$ such that $\binom{2n}{n}$ is coprime to $105$? Current best: The best result in this direction is due to Bloom and Croot [BlCr25], who proved that, if $p_1,p_2,p_3$ are sufficiently large primes, then there are infinitely many $n$ such that almost all of the base $p_i$ digits are $<p_i/2$. Prize: no. OEIS: A030979. Tags: base representations, binomial coefficients, number theory.