Decomposing Factorials into Large Factors: Progress on an Old Conjecture

2025-03-28
Decomposing Factorials into Large Factors: Progress on an Old Conjecture

A new paper studies the problem of factoring a factorial into factors as large as possible. Erdős and others proposed a conjecture about this, but the proof was lost. This paper, using clever applications of the prime number theorem and approximate factorization, provides new upper and lower bounds, partially solving this long-standing problem and offering new avenues to fully resolve the remaining conjectures.

Development combinatorics