On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products
AMERICAN MATHEMATICAL MONTHLY, vol.123, no.6, pp.597-599, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 123 Issue: 6
- Publication Date: 2016
- Doi Number: 10.4169/amer.math.monthly.123.6.597
- Journal Name: AMERICAN MATHEMATICAL MONTHLY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.597-599
- Middle East Technical University Northern Cyprus Campus Affiliated: Yes
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.