Catalan's conjecture
= Catalan's conjecture
{wiki=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) \\).