High Quality Content by WIKIPEDIA articles! In number theory, St rmer's theorem, named after Carl St rmer, gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell equations. It follows from the Thue–Siegel–Roth theorem that there are only a finite number of pairs of this type, but St rmer gave a procedure for finding them all. Louis Mordell wrote about this result, saying that it "is very pretty, and there are many applications of it."

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