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Pythagoras and the early Order initially treated number concretely, as patterns with pebbles, but over time the Pythagoreans developed and refined their concept of number into the same abstract entity which still ... Even today, existing Western cults refer to Pythagorean doctrines on number. According to Boyer [7]:
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www.mathgym.com.au/history/pythagoras/pythnum.htm
www.mathgym.com.au/history/pythagoras/pythnum.htm
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Forth algorithms, benchmarks ... The first perfect number after 6 is 28: {1, 2, 4, 7, 14}. The next are 496, 8,128, 33,550,336, 8,589,869,056. ... Pythagoras found that a perfect number is the sum of a series of consecutive rational numbers:
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home.iae.nl/users/mhx/perfect.html
home.iae.nl/users/mhx/perfect.html
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Prove that if there is an odd perfect number, then it is the hypotenuse of a Pythagorean triple. ... While the even perfect numbers have been an object of study from the time of Euclid, no odd perfect number has ever been found. No one was able to prove that they do not exist either;
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www.cut-the-knot.org/pythagoras/pythPerfect.shtml
www.cut-the-knot.org/pythagoras/pythPerfect.shtml
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Historically, Pythagoras means much more that the familiar theorem about right triangles. ... Also ascribed to the Pythagorean s is the study of perfect and amicable and deficient numbers. ... In addition, the number a was classified as abundant or deficient according as their divisors summed greater or less than a, respectively.
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www.math.tamu.edu/~dallen/history/pythag/pythag.html
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Perfect numbers were studied by Pythagoras and his followers, more for their mystical properties than for their number theoretic properties. Before we begin to look at the history of the study of perfect numbers, we define the concepts which are involved.
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www-history.mcs.st-and.ac.uk/HistTopics/Perfect_numbers...
www-history.mcs.st-and.ac.uk/HistTopics/Perfect_numbers.html
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* Of which island was Pythagoras a native? * Where did he settle in about 530 B.C.? * According to Pythagoras, which of the following had a real and separate existence outside our minds? * Which number was a perfect number, according to Pythagoras?
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www.funtrivia.com/quizzes/people/scientists__inventors/...
www.funtrivia.com/quizzes/people/scientists__inventors/pythagoras.html
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3. According to Pythagoras, which of the following had a real and separate existence outside our minds? ... 4. Which number was a perfect number, according to Pythagoras? ... 5. According to Pythagoras, the numbers 1, 3, 6, 10, etc. were called what?
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www.funtrivia.com/playquiz/quiz250792e20d0.html
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Let o(n) be the number theoretic function which denotes the sum of all divisors of a natural number n. If o(n) is an integral multiply of n, then n is denoted as a multiply perfect number or k-fold perfect number (also called multiperfect number or pluperfect number).
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wwwhomes.uni-bielefeld.de/achim/mpn.html
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The Pythagoreans beleived certain numbers held special properties. ... Those numbers whose factors added together equal the number themselves were perfect numbers. 6 is a perfect number because its factors (1 + 2 + 3) equal 6.
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ancienthistory.about.com/od/pythagoras/f/pythagoreannum...
ancienthistory.about.com/od/pythagoras/f/pythagoreannumb.htm
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