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2. By replacing f in Problem 1 with certain well-known multiplicative functions prove (a) lH(d)| = 2»(»), dịn (b) lu(d)\F(d) = 3-(m). %3D (c) ElH(d)\p(d) = [IP: This says that if we take the sum of p(d) over the squarefree divisors d of n, then we get the largest squarefree divisor of n.

2. By replacing f in Problem 1 with certain well-known multiplicative functions prove (a) lH(d)| = 2»(»), dịn (b) lu(d)\F(d) = 3-(m). %3D (c) ElH(d)\p(d) = [IP: This says that if we take the sum of p(d) over the squarefree divisors d of n, then we get the largest squarefree divisor of n.

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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No SIM 11:22 AM O 62% Thursday Edit 6:44 PM 1. Prove that if ƒ is multiplicative, then E lH(d)\f(d) = II(1+f(p)). pln Suggestion: Modify the proof of a similar result on page 5 of the notes. 2. By replacing f in Problem 1 with certain well-known multiplicative functions prove (a) \µ(d)| = 2(n). dn (b) \µ(d)|t(d) = 3~(n). dn (c) lu(d)lp(d) = I[p. dn pln This says that if we take the sum of p(d) over the squarefree divisors d of n, then we get the largest squarefree divisor of n.
Transcribed Image Text:No SIM 11:22 AM O 62% Thursday Edit 6:44 PM 1. Prove that if ƒ is multiplicative, then E lH(d)\f(d) = II(1+f(p)). pln Suggestion: Modify the proof of a similar result on page 5 of the notes. 2. By replacing f in Problem 1 with certain well-known multiplicative functions prove (a) \µ(d)| = 2(n). dn (b) \µ(d)|t(d) = 3~(n). dn (c) lu(d)lp(d) = I[p. dn pln This says that if we take the sum of p(d) over the squarefree divisors d of n, then we get the largest squarefree divisor of n.
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