Answered: Given a positive integer n, prove that…

Given a positive integer n, prove that E$(d) = n, u|p where the summation above runs over the set of positive divisors d of n. Hint: For a positive divisor d of n, define a set Sa = {m e Z | 1

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

Given a positive integer n, prove that
E$(d) = n,
d|n
where the summation above runs over the set of positive divisors d of n.
Hint: For a positive divisor d of n, define a set
Sa = {m E Z | 1 <m <n and (m, n) = d}.
To calculate |Sa| (the number of integers in the set Sa), recall that (m, n) = d
if and only if ( a) = 1.

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