On the Diophantine equation (x+1)(k) (x+2)(k) + . . . plus (lx)(k) = y(n)

SOYDAN G.

PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.91, ss.369-382, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 91
  • Basım Tarihi: 2017
  • Doi Numarası: 10.5486/pmd.2017.7679
  • Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.369-382
  • Anahtar Kelimeler: Bernoulli polynomials, high degree equations
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

Let k, l >= 2 be fixed integers. In this paper, firstly, we prove that all solutions of the equation (x + 1)(k) + (x + 2)(k) + . . . + (lx)(k) = y(n) in integers x,y,n with x, y >= 1, n >= 2 satisfy n < C-1, where C-1 = C-1(l, k) is an effectively computable constant. Secondly, we prove that all solutions of this equation in integers x, y, n with x,y >= 1,n >= 2, k not equal 3 and I 0 (mod 2) satisfy max{x, y, n} < C-2, where C-2 is an effectively computable constant depending only on k and I.