ADVANCED ENGINEERING MATHEMATICS
10th Edition
ISBN: 9781119664697
Author: Kreyszig
Publisher: WILEY
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Let Χ be a real-valued character (mod k). Let
k
S = Σnx(n).
n=1
If (a, k) = 1,
ax(a)S = S (mod k).
(iii) Write k = 2ºq where q is odd. Show that there is an integer a
with (a, k) = 1 such that a = 3 (mod 2ª) and a = 2 (mod q).
Deduce that 12S = 0 (mod k).
Prove that
(1) Σσς (α) μ(η/α) = n
d/n
(ii) Σσς(d) = η Σσο(α)/d
d❘n
d❘n
(iii) σ (d) σ (n/d) = Σ d³oo(d) σo(n/d).
d|n
dn
how to do part b,c
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