Some polynomial values binary recurrences

• Autores: László Szalay
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 35, Nº. 2, 2001, págs. 99-106
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We study the diophantine equations Gn = (?k)and Gn = ∑xi=1 ik in integers n ≥ 0 and x ≥ k (x ≥ 1) with fixed positive integer k, where Gn denotes the nth term of a binary recurrence of certain types. We give a simple practical algorithm which can solve the first equation if k = 3 and the second equation if k = 2. As a demonstration, this algorithm is applied to provide the solutions of the second equation in case of the Fibonacci, Lucas and Pell sequences. Further, using different methods, the problems Gn = (?4) and Gn = ∑xi=1 i3 will be solved for the three famous recurrences.