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  2. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ). Then its numerator and denominator are the sides, b and a, of a right triangle, and the hypotenuse is b + 1. For example:

  3. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4).

  4. Fermat's factorization method - Wikipedia

    en.wikipedia.org/wiki/Fermat's_factorization_method

    If the approximate ratio of two factors (/) is known, then a rational number / can be picked near that value. N u v = c v ⋅ d u {\displaystyle Nuv=cv\cdot du} , and Fermat's method, applied to Nuv , will find the factors c v {\displaystyle cv} and d u {\displaystyle du} quickly.

  5. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

  6. General number field sieve - Wikipedia

    en.wikipedia.org/wiki/General_number_field_sieve

    When using such algorithms to factor a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order n 1/2. The size of these values is exponential in the size of n (see below). The general number field sieve, on the other hand, manages to search for smooth numbers that are subexponential in the ...

  7. Kelly Clarkson Fans Say They've 'Been Waiting' For Her ... - AOL

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    One fan chimed in to say “I’ve been waiting for this one Kelly!!!” and another agreed, writing, “I lerv when you cover Chappell!!” while a third said, “I'm loving this @chappellroan ...

  8. Orthogonal array - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_Array

    k is the number of factors, v is the number of levels, t is the strength, and λ is the index. The definition of strength leads to the parameter relation N = λv t. An orthogonal array is simple if it does not contain any repeated rows. (Subarrays of t columns may have repeated rows, as in the OA(18, 7, 3, 2) example pictured in this section.)

  9. Lin-Manuel Miranda 'can't predict' hit 'Mufasa' song, is ...

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    "The fun on this one were the things I hadn't had a chance to do on another movie. So to get to write a romantic ballad for Disney, which you know Moana didn't have time for romance, neither did ...

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