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If m, n are relatively prime, then o(mn) = o(m)o(n)

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

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The Euler totient function is defined as ϕ (m) = |{k : 1 ≤ k ≤ m gcd(k, m) = 1}|, or rather the number of relatively prime positive integers smaller than or equal to m.

The Task is to prove the following:

If m, n are relatively prime, then o(mn) = o(m)o(n)

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