On the Greatest Prime Factor of Some Divisibility Sequences
Amir Akbary, Soroosh Yazdani · Contemporary mathematics - American Mathematical Society · 2015
Let P ( m ) P(m) denote the greatest prime factor of m m . For integer a > 1 a>1 , M. Ram Murty and S. Wong proved that, under the assumption of the ABC conjecture, \[ P ( a n − 1 ) ≫ ϵ , a n 2 − ϵ P(a^n-1)\gg _{\epsilon , a} n^{2-\epsilon } \] for any ϵ > 0 \epsilon >0 . We study analogues results for the corresponding divisibility sequence over the function field F q ( t ) \mathbb {F}_q(t) and for some divisibility sequences associated to elliptic curves over the rational field Q \mathbb {Q} .