On a Problem of Erdos and Graham

Yildiz B., Gurel E.

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, cilt.51, sa.2, ss.397-415, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00574-019-00158-9
  • Dergi Adı: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.397-415
  • Anahtar Kelimeler: Hypersurfaces, Integer points, Polynomials, Parametrizations, CONSECUTIVE INTEGERS, BLOCKS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

An old conjecture of Erdos and Graham states that only finitely many integer squares could be obtained from product of disjoint blocks of consecutive integers of length greater than or equal to four. It is known by counterexamples that the conjecture is false for product of disjoint blocks of four and five consecutive integers. In this paper, we present new algorithms generating new polynomial parametrizations that extend the polynomial parametrization given by Bennett and Luijk (Indag Math (N.S.) 23(1-2):123-127, 2012). Moreover, we produce the first examples of integer squares obtained from product of disjoint blocks of consecutive integers such that each block has length six or seven.