We study the behavior of the greatest common divisor of a k − 1 and b k − 1, where a, b are fixed integers or polynomials, and k varies. In the integer case, we conjecture that when a and b are multiplicatively independent and in addition a− 1 and b − 1 are coprime, then a k − 1 and b k − 1 are coprime infinitely often. In the polynomial case, we prove a… (More)
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