The Diophantine equation (x+1)(k) + (x+2)(k) + ... plus (lx)(k) = y(n) revisted

Bartoli D., Soydan G.

PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.96, sa.1-2, ss.111-120, 2020 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 96 Sayı: 1-2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.5486/pmd.2020.8604
  • Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.111-120
  • Anahtar Kelimeler: Bernoulli polynomials, high degree equations, PERFECT POWERS, SUMS
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

Let k,l >= 2 be fixed integers, and C be an effectively computable constant depending only on k and l. In this paper, 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, k not equal 3 and l 1 (mod 2) satisfy max{x, y, n} < C. The case when is even has already been completed by the second author (see [24]).