Brokardov problem
Brokardov problem je nerešen problem u matematici. Traže se prirodni brojevi n i m za koje važi
gde n! je faktorijel. Predložio ga je Henri Brokard u radovima iz 1876. i 1885, i nezavisno 1913. Srinivasa Ramanudžan.[1]
Reference
[uredi | uredi izvor]- ^ Berndt, Bruce C.; Galway, William F. (2000), „The Brocard–Ramanujan diophantine equation n! + 3 = m2” (PDF), The Ramanujan Journal, 4: 41—42, S2CID 119711158, doi:10.1023/A:1009873805276
Literatura
[uredi | uredi izvor]- 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
[uredi | uredi izvor]- 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.