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On Euler's Φ-Function and its Extensions
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The type of argument given in text-books to derive the form of Φ(n)-the number of numbers less than n and prime to n, is as follows. If n be the given number and p1, p2,...,pq be the different prime factors of n, then there are n/Pi numbers divisible by pi, n/pj numbers divisible by pj, and so on. Generally there are n/pipjpk..... numbers divisible by pi, pj, pk,......, simultaneously.
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