Catalan's conjecture

Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu. The integers 23 and 32 are two powers of natural numbers whose values (8 and 9, respectively) are consecutive. The theorem states that this is the only case of two consecutive powers. That is to say, that Catalan's conjecture — the only solution in the natural numbers of for a, b > 1, x, y > 0 is x = 3, a = 2, y = 2, b = 3.

Catalan's conjecture

Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu. The integers 23 and 32 are two powers of natural numbers whose values (8 and 9, respectively) are consecutive. The theorem states that this is the only case of two consecutive powers. That is to say, that Catalan's conjecture — the only solution in the natural numbers of for a, b > 1, x, y > 0 is x = 3, a = 2, y = 2, b = 3.