Exercise 8.3. Let c(n) denote Ramanujan's sum and let M(r)=En

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Exercise 8.3. Let c(n) denote Ramanujan's sum and let M(r) = En<++(n), the partial
sums of the Möbius function.
(a) Prove that
[alm) – EdM ().
TL
LCa (m)
k=1
In particular, when n = m, we have
Ca (m) =dM (G
d|m
(b) Use (a) to deduce that
H(m/d) Cx(d).
M(m) =
P
k=1
Transcribed Image Text:Exercise 8.3. Let c(n) denote Ramanujan's sum and let M(r) = En<++(n), the partial sums of the Möbius function. (a) Prove that [alm) – EdM (). TL LCa (m) k=1 In particular, when n = m, we have Ca (m) =dM (G d|m (b) Use (a) to deduce that H(m/d) Cx(d). M(m) = P k=1
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