2. An investigation of perfect numbers Our goal is to give a proof of the following:2m-1(2m –1),Theorem: Suppose n is an even perfect number, then n has the form n =where 2m – 1 is a prime.(a) In class we proved that (rk * U)(n) = ok(n), showing that the arithmetic functionOk is multiplicative. Deduce a formula for ok(p°) where p is a prime and e is somenatural number.Hint: List all the divisors of pº, notice that the sum of their kth powers forms ageometric summation and recall that a geometric summation has closed form--()1as= aS- 1j=0What are the numbers a and s in this example?

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Description: 2. An investigation of perfect numbers Our goal is to give a proof of the following:2m-1(2m –1),Theorem: Suppose n is an even perfect number, then n has the form n =where 2m – 1 is a prime.(a) In class we proved that (rk * U)(n) = ok(n), showing tha

It is given that 2m-1 is prime. Hence the number n=2m-12m-1 has only two prime factors which are: 2…

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2. An investigation of perfect numbers Our goal is to give a proof of the following: Theorem: Suppose n is an even perfect number, then n has the form n = where 2m – 1 is a prime. 2m-1(2m –1), (a) In class we proved that (rk * U)(n) = ok(n), showing that the arithmetic function Ok is multiplicative. Deduce a formula for o6(p°) where p is a prime and e is some natural number. Hint: List all the divisors of pº, notice that the sum of their kth powers forms a geometric summation and recall that a geometric summation has closed form gl+1 asi = a S - 1 j=0

2. An investigation of perfect numbers Our goal is to give a proof of the following: Theorem: Suppose n is an even perfect number, then n has the form n = where 2m – 1 is a prime. 2m-1(2m –1), (a) In class we proved that (rk * U)(n) = ok(n), showing that the arithmetic function Ok is multiplicative. Deduce a formula for o6(p°) where p is a prime and e is some natural number. Hint: List all the divisors of pº, notice that the sum of their kth powers forms a geometric summation and recall that a geometric summation has closed form gl+1 asi = a S - 1 j=0

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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