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  2. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4; that is, each prime factor has the form 4n + 1. In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c ...

  3. Pythagoreanism - Wikipedia

    en.wikipedia.org/wiki/Pythagoreanism

    Pythagorean philosophers investigated the relationship of numbers extensively. They defined perfect numbers as those that were equal to the sum of all their divisors. For example: 28 = 1 + 2 + 4 + 7 + 14. [32] The theory of odd and even numbers was central to Pythagorean arithmetic. This distinction was for the Pythagorean philosophers direct ...

  4. Pythagoras number - Wikipedia

    en.wikipedia.org/wiki/Pythagoras_number

    In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p ( K ) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares.

  5. Numerology - Wikipedia

    en.wikipedia.org/wiki/Numerology

    Numerology (known before the 20th century as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in words and names. When numerology is applied to a person's name, it is a form of onomancy.

  6. Pythagorean prime - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_prime

    However, the number of Pythagorean primes up to is frequently somewhat smaller than the number of non-Pythagorean primes; this phenomenon is known as Chebyshev's bias. [1] For example, the only values of n {\displaystyle n} up to 600000 for which there are more Pythagorean than non-Pythagorean odd primes less than or equal to n are 26861 and 26862.

  7. Tetractys - Wikipedia

    en.wikipedia.org/wiki/Tetractys

    For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all. [5] The Pythagorean oath also mentioned the Tetractys: By that pure, holy, four lettered name on high,

  8. Group of rational points on the unit circle - Wikipedia

    en.wikipedia.org/wiki/Group_of_rational_points...

    The Pythagorean triple (4,3,5) is associated to the rational point (4/5,3/5) on the unit circle. In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x 2 + y 2 = 1. The set of such points turns out to be closely related to primitive Pythagorean triples.

  9. Pythagorean quadruple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_quadruple

    A Pythagorean quadruple is called primitive if the greatest common divisor of its entries is 1. Every Pythagorean quadruple is an integer multiple of a primitive quadruple. The set of primitive Pythagorean quadruples for which a is odd can be generated by the formulas = +, = (+), = (), = + + +, where m, n, p, q are non-negative integers with greatest common divisor 1 such that m + n + p + q is o

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