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A Neighboring-Denominator Variant of the Erdős--Mahler Conjecture
We prove a quantitative neighboring-denominator variant of the Erdős-Mahler conjecture. Let $p_n/q_n$ be the convergents of an irrational real number $ξ$. If $p_nq_nq_{n+1}$ is $S$-smooth for infinitely many $n$, where $S$ is a fixed finite set of primes, then there exists an effectively computable
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