On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products


Gurel E.

AMERICAN MATHEMATICAL MONTHLY, vol.123, no.6, pp.597-599, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 123 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.4169/amer.math.monthly.123.6.597
  • Title of Journal : AMERICAN MATHEMATICAL MONTHLY
  • Page Numbers: pp.597-599

Abstract

We prove that the product of first n consecutive values of the polynomial P(k) = 4k(4) + 1 is a perfect square infinitely often whereas the product of first n consecutive values of the polynomial Q(k) = k(4) + 4 is a perfect square only for n = 2.