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Prove each of the following statements. (a) If q is a prime number not equal to 3 and k = 3q, then o(k) = 2 (T(k)+ ¢(k)). (b) If q is an odd prime number and k = 2q, then k = o(k) – T(k) – o(k).

Prove each of the following statements. (a) If q is a prime number not equal to 3 and k = 3q, then o(k) = 2 (T(k)+ ¢(k)). (b) If q is an odd prime number and k = 2q, then k = o(k) – T(k) – o(k).

Advanced Engineering Mathematics
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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7. Prove each of the following statements. (a) If \( q \) is a prime number not equal to 3 and \( k = 3q \), then \( \sigma(k) = 2 \left( \tau(k) + \phi(k) \right) \). (b) If \( q \) is an odd prime number and \( k = 2q \), then \( k = \sigma(k) - \tau(k) - \phi(k) \).
Transcribed Image Text:7. Prove each of the following statements. (a) If \( q \) is a prime number not equal to 3 and \( k = 3q \), then \( \sigma(k) = 2 \left( \tau(k) + \phi(k) \right) \). (b) If \( q \) is an odd prime number and \( k = 2q \), then \( k = \sigma(k) - \tau(k) - \phi(k) \).
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