Let n e N.(a) Prove thatSp(n) if n is odd;20(n) if n is even.p(2n) :(b) Generalize (2n) = 2p(n) for all even n by showing that p(mn) = mp(n) ifevery prime divisor of m is a prime divisor of n.

Here we use the formula φ(n)=n∏p|n1-1p.

Answered: (а) Prove that p(n) p(2n) = if n is…

(а) Prove that p(n) p(2n) = if n is odd; 24(n) if n is even. (b) Generalize ç(2n) = 24(n) for all even n by showing that p(mn) = every prime divisor of m is a prime divisor of n. то(п) if

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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Question

Let n e N.
(a) Prove that
Sp(n) if n is odd;
20(n) if n is even.
p(2n) :
(b) Generalize (2n) = 2p(n) for all even n by showing that p(mn) = mp(n) if
every prime divisor of m is a prime divisor of n.

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