On the range of Carmichael’s universal-exponent function
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چکیده
Let λ denote Carmichael’s function, so λ(n) is the universal exponent for the multiplicative group modulo n. It is closely related to Euler’s φ-function, but we show here that the image of λ is much denser than the image of φ. In particular the number of λ-values to x exceeds x/(log x).36 for all large x, while for φ it is equal to x/(log x)1+o(1), an old result of Erdős. We also improve on an earlier result of the first
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تاریخ انتشار 2013