Products of disjoint blocks of consecutive integers which are powers

Volume 98 / 2003

Mariusz Skałba Colloquium Mathematicum 98 (2003), 1-3 MSC: 11A05, 11D57. DOI: 10.4064/cm98-1-1


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~$x$.


  • Mariusz SkałbaDepartment of Mathematics, Computer Science and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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