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Products of disjoint blocks of consecutive integers which are powers

Mariusz Skałba (2003)

Colloquium Mathematicae

The product of consecutive integers cannot be a power (after Erdős and Selfridge), but products of disjoint blocks of consecutive integers can be powers. Even if the blocks have a fixed length l ≥ 4 there are many solutions. We give the bound for the smallest solution and an estimate for the number of solutions below x.

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