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

Gurel E.

AMERICAN MATHEMATICAL MONTHLY, cilt.123, sa.6, ss.597-599, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 123 Sayı: 6
  • Basım Tarihi: 2016
  • Doi Numarası: 10.4169/amer.math.monthly.123.6.597
  • Dergi Adı: AMERICAN MATHEMATICAL MONTHLY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.597-599
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.