Resumen de On the Greatest Common Divisor of u - 1 and v - 1 with u and v Near S-units

Florian Luca

• In [2], it was shown that if a and b are multiplicatively independent integers and ? > 0, then the inequality gcd (an - 1,bn - 1) < exp(?n) holds for all but finitely many positive integers n. Here, we generalize the above result. In particular, we show that if f(x),f1(x),g(x),g1(x) are non-zero polynomials with integer coefficients, then for every ? > 0, the inequality holds for all but finitely many positive integers n