Euler indicators of binary recurrence sequences

• Autores: Florian Luca
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 53, Fasc. 2, 2002, págs. 133-156
• Idioma: inglés
• Títulos paralelos:
  • Indicadores de Euler de sucesiones binarias por recurrencia
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we show that if $(u_n)_n\geq 0$ and $(v_n)_n\geq 0$ are two non-degenerate binary recurrent sequences of integers such that $(v_n)_n\geq 0$ satisfies some technical assumptions, then the diophantine equation $\vert v_n\vert = \phi(\vert u_m\vert)$ has only finitely many effectively computable positive integer solutions $(m,n)$. Here, for a nonzero integer $k$ we use $\phi(k)$ to denote the Euler function of $k$.