Tijdeman's Theorem

Tijdeman's theorem, proved by the Dutch number theorist Robert Tijdeman in 1976 using Baker's method from transcendental number theory, states that the equation y to the m equals x to the n plus 1, with both exponents greater than one, has only finitely many integer solutions, and it gives an effective upper bound on those solutions, though Michel Langevin later computed a bound so large it offered little practical help. The theorem provided a strong impetus toward the eventual proof of Catalan's conjecture, which Preda Mihailescu completed by narrowing the possibilities down to the single known consecutive-power pair, 9 equals 8 plus 1.