Products of disjoint blocks of consecutive integers which are powers

• Autorzy: Mariusz Skałba
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors
• 11D57: Multiplicative and norm form equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 98
• Numer: 1
• Strony: 1-3

Daty

wydano

2003

Twórcy

autor

Mariusz Skałba

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

Identyfikatory

DOI

10.4064/cm98-1-1