{"id":"palomar/PALOMAR-2026-11-02-000011","url":"https://github.com/veljjanoski/erdos393-palomar/tree/ec05768609980a27995453bc1701e6fa3004d675","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-02-000011-v1.json","repo":"https://github.com/veljjanoski/erdos393-palomar","tags":["math.NT","msc:11D85","msc:11B65"],"score":0,"title":"Erdős Problem 393: f(n) tends to infinity, assuming the abc conjecture","trust":"high","domain":"math.NT","source":"palomar","authors":["Daniel Veljjanoski"],"reviews":0,"subject":"math.NT","summary":"Let f(n) be the least m >= 1 such that n! = a_1 ... a_t with a_1 = n!. It does not assume Luca's theorem; only the reduction from f(n) to these polynomials is specific to Problem 393.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-02","reactions":{},"formalized":true,"formalizes":[{"title":"The Diophantine equation P(x) = n! and a result of M. Overholt","identifier":"","relationship":"adapts"},{"title":"Erdős Problem 393","identifier":"","relationship":"formalizes"}]}