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

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Gurel E.

AMERICAN MATHEMATICAL MONTHLY, vol.123, no.6, pp.597-599, 2016 (SCI-Expanded)

• 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 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.