About Brocard's Problem
The Problem
Find integer solutions to the equation: n! + 1 = m²
Only three solutions are known: (4,5), (5,11), and (7,71)
Known Solutions
n = 4: 4! + 1 = 24 + 1 = 25 = 5²
n = 5: 5! + 1 = 120 + 1 = 121 = 11²
n = 7: 7! + 1 = 5040 + 1 = 5041 = 71²
The Challenge
No other solutions are known for n < 10⁹. Finding a fourth solution would be a major discovery!