A note on the products ((<i>m</i>+1)<SUP>2</SUP>+1)((<i>m</i>+2)<SUP>2</SUP>+1) ... (<i>n</i><SUP>2</SUP>+1) and ((<i>m</i>+1)<SUP>3</SUP>+1)((<i>m</i>+2)<SUP>3</SUP>+1) ... (<i>n</i><SUP>3</SUP>+1)

GÜREL E.

MATHEMATICAL COMMUNICATIONS, vol.21, no.1, pp.109-114, 2016 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 1
  • Publication Date: 2016
  • Journal Name: MATHEMATICAL COMMUNICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.109-114
  • Middle East Technical University Northern Cyprus Campus Affiliated: Yes

Abstract

We prove that for any positive integer m there exists a positive real number N-m such that whenever the integer n >= m neither the product P-m(n) = ((m + 1)(2) + 1) ((m + 2)(2) + 1) ... (n(2) + 1) nor the product Q(m)(n) = ((m + 1)(3) + 1)((m + 2)(3) + 1) ... (n(3) + 1) is a square.