Catalan's conjecture

Catalan's conjecture, also known as Mihăilescu's theorem, states that the only solution in positive integers to the equation \( x^a - y^b = 1 \), where \( a \) and \( b \) are integers greater than 1, is the pair \( (3, 2) \) for the values \( (x, y) \) and \( (a, b) = (3, 2) \).