= A positive integer is called perfect if it is equal to the sum of its positive divisors other than itself. (For example, 6 is perfect as 6 1+2+3.) For an integer n, prove that if 2n 1 is prime then 2n-1(2n – 1) is perfect. - [10 marks]
= A positive integer is called perfect if it is equal to the sum of its positive divisors other than itself. (For example, 6 is perfect as 6 1+2+3.) For an integer n, prove that if 2n 1 is prime then 2n-1(2n – 1) is perfect. - [10 marks]
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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Question
A positive integer is called perfect if it is equal to the sum of its positive divisors other than itself. (For example, 6 is perfect as 6 = 1 + 2 + 3.) For an integer n, prove that if 2^(n) − 1 is prime then 2^(n−1)(2^(n) − 1) is perfect.
![A positive integer is called perfect if it is equal to the sum of its positive divisors
other than itself. (For example, 6 is perfect as 6 = 1+2+3.) For an integer n,
prove that if 2n - 1 is prime then 2n-1(2n – 1) is perfect.
[10 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3540d6de-ad37-46d3-bbb2-d527fb41b178%2F7771d40a-4b40-47aa-af38-dfabbfdb87a6%2Fkbwykxc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A positive integer is called perfect if it is equal to the sum of its positive divisors
other than itself. (For example, 6 is perfect as 6 = 1+2+3.) For an integer n,
prove that if 2n - 1 is prime then 2n-1(2n – 1) is perfect.
[10 marks]
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