n Let F(n) = 2πία е п Show that F(1) = 1 and F(n) = 0 for all n > 1. a=1

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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n
2πία
3. (a) Let F(n) =£
Show that F(1) = 1 and F(n) = 0 for all n > 1.
a=1
(b) For all positive integers n, show that the value of un is the sum of the primitive
nth roots of unity. That is to say,
2πία
H(12) = E
Σ
e
n
gcd(a,n)=1
where the sum ranges from a = 1 to a = n.
Transcribed Image Text:n 2πία 3. (a) Let F(n) =£ Show that F(1) = 1 and F(n) = 0 for all n > 1. a=1 (b) For all positive integers n, show that the value of un is the sum of the primitive nth roots of unity. That is to say, 2πία H(12) = E Σ e n gcd(a,n)=1 where the sum ranges from a = 1 to a = n.
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