High Quality Content by WIKIPEDIA articles! In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equation ym = xn + 1, for exponents n and m greater than one, is finite. The theorem was proven by Dutch number theorist Robert Tijdeman in 1976, and provided a strong impetus towards the eventual proof of Catalan's conjecture by Preda Mihailescu. Mihailescu's theorem states that there is only one member to the set of consecutive power pairs, namely 9=8+1.

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