Complete resolution of the polynomial analogue of the Brocard–Ramanujan problem in mathematics

Dr. Wataru Takeda, Department of Mathematics at the Faculty of Science, Toho University, has completely solved the polynomial analogue of the long-standing Brocard–Ramanujan problem, originally proposed in 1876 and still unsolved in its integer form. The study appears in the February 2026 issue of the journal Finite Fields and Their Applications.

Key Points

• Complete solution of the polynomial analogue of the Brocard–Ramanujan problem, originally proposed in 1876 by the French mathematician Henri Brocard.
• The original integer version of the Brocard–Ramanujan problem remains unsolved, and this breakthrough in the polynomial setting is expected to provide key insights toward solving the classical problem.

Journal:
Finite Fields and Their Applications (Volume 110, February 2026; online publication: September 30, 2025)
 

Title:
Brocard–Ramanujan problem for polynomials over finite fields
 

Author:
Wataru Takeda*
 

DOI:
10.1016/j.ffa.2025.102731