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  2. Ruth–Aaron pair - Wikipedia

    en.wikipedia.org/wiki/Ruth–Aaron_pair

    Any Ruth–Aaron pair of square-free integers belongs to both lists with the same sum of prime factors. The intersection also contains pairs that are not square-free, for example (7129199, 7129200) = (7×11 2 ×19×443, 2 4 ×3×5 2 ×13×457).

  3. Formulas for generating Pythagorean triples - Wikipedia

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

    From this we see that r is any even integer and that s and t are factors of r 2 /2. All Pythagorean triples may be found by this method. When s and t are coprime, the triple will be primitive. A simple proof of Dickson's method has been presented by Josef Rukavicka, J. (2013). [7] Example: Choose r = 6. Then r 2 /2 = 18. The three factor-pairs ...

  4. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    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. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...

  5. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    For example, if n = 171 × p × q where p < q are very large primes, trial division will quickly produce the factors 3 and 19 but will take p divisions to find the next factor. As a contrasting example, if n is the product of the primes 13729, 1372933, and 18848997161, where 13729 × 1372933 = 18848997157, Fermat's factorization method will ...

  6. Amicable numbers - Wikipedia

    en.wikipedia.org/wiki/Amicable_numbers

    However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65.

  7. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).

  8. Today's Wordle Hint, Answer for #1252 on Friday, November 22 ...

    www.aol.com/todays-wordle-hint-answer-1252...

    Today's Wordle Answer for #1252 on Friday, November 22, 2024. Today's Wordle answer on Friday, November 22, 2024, is PEARL. How'd you do? Next: Catch up on other Wordle answers from this week.

  9. Complex conjugate root theorem - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate_root_theorem

    The non-real factors come in pairs which when multiplied give quadratic polynomials with real coefficients. Since every polynomial with complex coefficients can be factored into 1st-degree factors (that is one way of stating the fundamental theorem of algebra ), it follows that every polynomial with real coefficients can be factored into ...

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