摘要
Let f and g be algebraically independent entire functions. We first give an estimate of the Nevanlinna counting function for the common zeros of f n -1 and g n -1 for sufficiently large n. We then apply this estimate to study divisible sequences in the sense that f n - 1 is divisible by g n - 1 for infinitely many n. For the first part of establishing our gcd estimate, we need to formulate a truncated second main theorem for effective divisors by modifying a theorem from a paper by Hussein and Ru and explicitly computing the constants involved for a blowup of P1 ×P1 along a point with its canonical divisor and the pull-back of vertical and horizontal divisors of P1 × P1.