Brocard’s problem

Brocard’s problem, first posed by Henri Brocard in 1876, asks for factorials that are one less than a square, that is, solutions to the equation $n!+1=m^{2}$ . Only three solutions are known: $4!+1=5^{2}$ , $5!+1=11^{2}$ and $7!+1=71^{2}$ . Srinivasa Ramanujan also pondered the problem, in 1913. Erdős believed that there are no other solutions, and no more have been found for $n$ up to $10^{9}$ .

References

1 P. Erdős, & R. OblÃÂ¡th, “Über diophantische Gleichungen der Form $n!=x^{p}\\pm y^{p}$ und $n!\\pm m!=x^{p}$ ” Acta Szeged. 8 (1937): 241 - 255

单词	BrocardsProblem
释义	Brocard’s problem Brocard’s problem, first posed by Henri Brocard in 1876, asks for factorials that are one less than a square, that is, solutions to the equation $n!+1=m^{2}$ . Only three solutions are known: $4!+1=5^{2}$ , $5!+1=11^{2}$ and $7!+1=71^{2}$ . Srinivasa Ramanujan also pondered the problem, in 1913. Erdős believed that there are no other solutions, and no more have been found for $n$ up to $10^{9}$ . References 1 P. Erdős, & R. OblÃÂ¡th, “Über diophantische Gleichungen der Form $n!=x^{p}\\pm y^{p}$ und $n!\\pm m!=x^{p}$ ” Acta Szeged. 8 (1937): 241 - 255
随便看	CoordinateSystems coordinate systems CoordinateVector coordinate vector CoordinateWay coordinate way CopelandErdHosConstant Copeland-Erdős constant CopositiveMatrix copositive matrix Coprime coprime Coproducts Coproduct types Copula copula CoreOfASubgroup core of a subgroup CornerOfARing corner of a ring CornerPointTheorem corner point theorem CorollariesOfBasicTheoremOnOrderedGroups corollaries of basic theorem on ordered groups CorollaryOfBanachAlaogluTheorem