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Let r ER andne N. Prove, by induction on n, that p" -1= (r – 1) · (r"-1 + r"-2 +...+r+1)

Let r ER andne N. Prove, by induction on n, that p" -1= (r – 1) · (r"-1 + r"-2 +...+r+1)

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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1 Let r eR and n E N. Prove, by induction on n, that pn – 1= (r – 1) · (r"-1 + r"-2 +...+r+1) Let n eN be such that p = 2"- 1 is a prime number (e.g., n = 2,3, 5, etc.) Define N = 2"-'p. List all positive integers which divide N. Prove that the sum of all positive divisors, including 1 but not N, is equal to N.
Transcribed Image Text:1 Let r eR and n E N. Prove, by induction on n, that pn – 1= (r – 1) · (r"-1 + r"-2 +...+r+1) Let n eN be such that p = 2"- 1 is a prime number (e.g., n = 2,3, 5, etc.) Define N = 2"-'p. List all positive integers which divide N. Prove that the sum of all positive divisors, including 1 but not N, is equal to N.
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