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Størmer's theorem states that for any fixed finite set $S$ of primes, there are only finitely many pairs of consecutive positive integers whose prime factors all belong to $S$. Equivalently, the equation $y-x=1$ has only finitely many solutions in positive $S$-smooth integers.

For $S=\{2,3\}$, the pairs include $(1,2),(2,3),(3,4)$ and $(8,9)$. The underlying method reduces the search to finitely many Pell equations by separating square factors from the products of allowed primes. The allowed prime set must stay fixed; allowing it to grow with the candidate integers would remove the finiteness assertion.