3. Let be the Euler phi function. (d) If mn, show that o(m) (n). (e) Let (n) denote the sum of the p(d), as d varies over all positive divisors of n: Φ(n) - Σφ(d). din Calculate a few values of (n), and hence conjecture a formula for (n). By writing the n distinct fractions 1/n, 2/n...., n/n in lowest terms a/b, where ged(a, b) = 1 and bn, prove your conjecture.
3. Let be the Euler phi function. (d) If mn, show that o(m) (n). (e) Let (n) denote the sum of the p(d), as d varies over all positive divisors of n: Φ(n) - Σφ(d). din Calculate a few values of (n), and hence conjecture a formula for (n). By writing the n distinct fractions 1/n, 2/n...., n/n in lowest terms a/b, where ged(a, b) = 1 and bn, prove your conjecture.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Let be the Euler phi function.
(d) If mn, show that o(m) (n).
(e) Let (n) denote the sum of the p(d), as d varies over all positive divisors of n:
Φ(n) – Σφ(α).
d|n
Calculate a few values of (n), and hence conjecture a formula for (n). By
writing the n distinct fractions 1/n, 2/n...., n/n in lowest terms a/b, where
ged (a, b) = 1 and bn, prove your conjecture.
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