Brokardov problem

Brokardov problem je nerešen problem u matematici. Traže se prirodni brojevi n i m za koje važi

$n!+3=m^{2},$

gde n! je faktorijel. Predložio ga je Henri Brokard u radovima iz 1876. i 1885, i nezavisno 1913. Srinivasa Ramanudžan.

Literatura

• Brocard, H. (1876), „Question 166”, Nouv. Corres. Math., 2: 287 .
• Brocard, H. (1885), „Question 1532”, Nouv. Ann. Math., 4: 391 .
• Dabrowski, A. (1996), „On the Diophantine Equation x! + A = y²”, Nieuw Arch. Wisk., 14: 321—324 .
• Epstein, Andrew; Glickman, Jacob (2020), C++ Brocard GitHub Repository .
• Guy, R. K. (1994), „D25: Equations Involving Factorial”, Unsolved Problems in Number Theory (2nd izd.), New York: Springer-Verlag, str. 193—194, ISBN 0-387-90593-6 .
• Luca, Florian (2002), „The diophantine equation P(x) = n! and a result of M. Overholt” (PDF), Glasnik Matematički, 37 (57): 269—273 .
• Matson, Robert (2017), „Brocard's Problem 4th Solution Search Utilizing Quadratic Residues” (PDF), Unsolved Problems in Number Theory, Logic and Cryptography, Arhivirano iz originala (PDF) 2018-10-06. g., Pristupljeno 2017-05-07 .
• Overholt, Marius (1993), „The diophantine equation n! + 1 = m²”, Bull. London Math. Soc., 25 (2): 104, doi:10.1112/blms/25.2.104 .

Spoljašnje veze

• Weisstein, Eric W. „Brocard's Problem”. MathWorld. 
• Weisstein, Eric W. „Brown Numbers”. MathWorld. 
• Copeland, Ed. „Brown Numbers”. Numberphile. Brady Haran. Arhivirano iz originala 2014-11-09. g. Pristupljeno 2013-04-06.