Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Perfect Number


Date: 7/21/96 at 14:57:47
From: EDSON TADEU
Subject: Perfect Number

How can I find a perfect number? What are some reference books for 
number theory?

Thank you!


Date: 8/2/96 at 13:37:21
From: Doctor Tom
Subject: Re: Perfect Number

There are hundreds of books on number theory.  Take a look in any 
library or bookstore, and find one that looks interesting to you.

A perfect number is a number such that if you add up all the divisors 
including 1 and the number itself, you get twice the number:

6 is perfect, since 1, 2, 3, and 6 are the divisors, and
1+2+3+6 = 12 = 2*6

28 is perfect, since 1, 2, 4, 7, 14, and 28 are the divisors, and 
1+2+4+7+14+28 = 56 = 2*28.

8 is not perfect, since 1, 2, 4, and 8 are the divisors, but
1+2+4+8= 15, which is not 2*8.

If 2^n-1 is prime (has no divisors), then
(2^(n-1))(2^n - 1) is perfect. (The "^" represents an exponent.)

As examples, 2^3-1 = 7, a prime, so (2^2)*(2^3-1) = 4*7 = 28 is
perfect.

All even perfect numbers have the form above.  Nobody knows if there 
are any odd perfect numbers.  If you can find one, or prove that 
there aren't any, you'll be famous!

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Number Theory
Middle School Number Sense/About Numbers

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/