B. Dahan

Sieve dimension and search depth for the Erd\H{o}s-Straus conjecture, $n \equiv 1 \pmod{24}$

For primes $n\equiv1\pmod{24}$ we study how deep an explicit, factorization-free search for a decomposition of $4/n$ into three unit fractions has to go. Write $E_2(N;J)$ for the set of such primes $n\le N$ at which no witness of depth at most $J$ exists, in the sense of the two-parameter criterion of Theorem 3.9 with...