18. Show that Ein d(k)³ = (Ekin d(k))² for all positive intege m

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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= n for all n, where T(n) = d(n)
17. prove that Edn H(n/d)T(d) = 1 and Edn H(n/d)o(d)
and σ(n)- σι (n) Σaμ d.
18. Show that Ekin d(k)³ = (Dkln d(k))² for all positive integer n.
19. Prove that Edn H(d) log™ d = 0 if m >1 and n has more than m distinct prime factors.
Transcribed Image Text:= n for all n, where T(n) = d(n) 17. prove that Edn H(n/d)T(d) = 1 and Edn H(n/d)o(d) and σ(n)- σι (n) Σaμ d. 18. Show that Ekin d(k)³ = (Dkln d(k))² for all positive integer n. 19. Prove that Edn H(d) log™ d = 0 if m >1 and n has more than m distinct prime factors.
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