Perfect Number

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perfect number

[′pər·fikt ′nəm·bər]
(mathematics)
An integer which equals the sum of all its factors other than itself.

Perfect Number

 

a positive integer that is equal to the sum of all its factors except itself. Examples of perfect numbers are 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14.

As early as the third century B.C., Euclid showed that even perfect numbers could be obtained from the formula 2p–l(2p – 1) when p and 2p – 1 are prime numbers. Approximately 20 even perfect numbers have been found in this way. As of 1976, no odd perfect numbers are known, and their existence remains an open question. Perfect numbers were first investigated by the Pythagoreans, who ascribed a special mystical meaning to such numbers and combinations of such numbers.

perfect number

equal in value to the sum of those natural numbers that are less than the given number but that also divide (with zero remainder) the given number. [Math.: EB, VII: 872]
References in periodicals archive ?
If a girl's name could be arranged, by choosing all or any part of it including initials, so that its number value is that of one of the pair, and if the boy's name could be written so that it has the number value of the other perfect number, their union would result in a perfect marriage.
For example 6 is the first perfect number 1+2+3+6=2x6=12 Note that 1/6 + 2/6 + 3/6 = 1 The next Perfect Number is 28 as 1+2+4+7+14+28=2x28=56 The first four Perfect Numbers 6, 28, 496, 8128 were the only ones known to Greek mathematicians and it was not until the 15th Century that mathematicians discovered other Perfect Numbers.
He then turns to topics that are particularly attractive and accessible, including Gauss' theory of cyclotomy and its applications to rational reciprocity laws; Hilbert's solution to Waring's problem; and modern work on perfect numbers.
Bege, On multiplicatively unitary perfect numbers, Seminar on Fixed Point Theory,
Besides, two new conjectures regarding the existence and non-existence of perfect numbers had been proposed by Kalita.
Key Words: Triangular numbers, Perfect square, Pascal Triangles, and perfect numbers.
Perfect numbers (PNs) are integers whose factors sum to the number, like 6 (=1+2+3).
To illustrate the seemingly simple, yet difficult, problems that fascinated Pythagoras, it is only necessary to point out that a large number of perfect numbers are known (6, 28, and 496 are the smallest) but that none of them are odd.
These perfect numbers are also attested by Euphorion in the Mopsopia, when he says: `.
And overhear the planets, as they raced along, Harmonize their pathways' perfect numbers.
received a $25,000 award for his investigation of the odd perfect number problem, and his suggestion that odd perfect numbers do not exist.
There are 10 chapters: surrealist writing, mathematical surfaces, and new geometries; objects, axioms, and constraints; abstraction in art, literature, and mathematics; literature, the Mobius strip, and infinite numbers; Klein forms and the fourth dimension; paths, graphs, and texts; poetry, permutations, and ZeckendorfAEs theorem; randomness, arbitrariness, and perfect numbers.