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

• Autores: Florian Luca
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 146, Nº 3, 2005, págs. 239-256
• Idioma: inglés
• DOI: 10.1007/s00605-005-0303-6
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• Resumen

  • 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