Does the equation n!+1=m^2 have any solutions with n,m∈N other than n=4,5,7? Equivalently, is n∈N:exists m∈N, n!+1=m^2=4,5,7?

Erdős Problem #398 — Brocard’s Factorial Square Equation

Does the equation $n!+1=m^2$ have any solutions with $n,m\in\mathbb{N}$ other than $n=4,5,7$ ? Equivalently, is

\{n\in\mathbb{N}:\exists m\in\mathbb{N},\ n!+1=m^2\}=\{4,5,7\}?

References

Posted 1 month ago · edited 3 weeks ago

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