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4. Exercise §5.2 #20 [This exercise presen Theorem 5.9 using the Möbius Inversion Form to that in Theorem 5.9] Let d be a positive di

4. Exercise §5.2 #20 [This exercise presen Theorem 5.9 using the Möbius Inversion Form to that in Theorem 5.9] Let d be a positive di

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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4. Exercise §5.2 #20 (This exercise presents a shorter and more elegant way to prove f(d) = ¢(d) in Theorem 5.9 using the Möbius Inversion Formula (Theorem 3.15). All notation in this exercise is identical to that in Theorem 5.9) Let d be a positive divisor of p – 1. (a) Prove that E (c) = d eld, d>0 (b) Use part (a) and the Möbius Inversion Formula to prove that ed, d>0
Transcribed Image Text:4. Exercise §5.2 #20 (This exercise presents a shorter and more elegant way to prove f(d) = ¢(d) in Theorem 5.9 using the Möbius Inversion Formula (Theorem 3.15). All notation in this exercise is identical to that in Theorem 5.9) Let d be a positive divisor of p – 1. (a) Prove that E (c) = d eld, d>0 (b) Use part (a) and the Möbius Inversion Formula to prove that ed, d>0
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