Products of disjoint blocks of consecutive integers which are powers
Volume 98 / 2003
Colloquium Mathematicum 98 (2003), 1-3
MSC: 11A05, 11D57.
DOI: 10.4064/cm98-1-1
Abstract
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 $l\geq 4$ there are many solutions. We give the bound for the smallest solution and an estimate for the number of solutions below~$x$.
