Establish the following properties of the Euler function , (a) If p is prime and n >
Question:
Establish the following properties of the Euler function φ,
(a) If p is prime and n > 0, then φ(pn) = pn(1- 1/p) = pn(1-1/p).
(b) If (m, n) = 1, then φ(mn) = φ(m)φ(n).
(c) If n = p1k1. • •prkr (pi distinct primes; ki > O), then φ(n) = n(1 - 1/p1) (1 - 1/p2)· · ·(1 - 1/pr).
(d)
(e)
Transcribed Image Text:
Σφ(α) = n. dẫn
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ANSWER a If p is prime and n 0 then pn pn1 1p To establish this property we need to understand the Eulers totient function n The Eulers totient functi...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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