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 divisorsother 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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= 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.

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