$x!+1=y^2$, I found 3 solutions. They are $(4,5),(5,11),(7,71)$. Is there a $4$th solution?If not can you prove it?
2026-04-01 06:29:07.1775024947
Can you find it? or Can you prove it?
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The same question has been asked before here. What you have asked is still an open question in Mathematics.
As stated in the wikipedia article Brocard's Problem, Overholt (1993) showed that there are only finitely many solutions provided that the abc conjecture is true. There is now under evaluation a proof of the abc conjecture by Shinichi Mochizuki.