Perfect NumberDate: 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/ |
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