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  2. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...

  3. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    Modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. [3] For this purpose, even for factoring over the rational numbers and number fields , a fundamental step is a factorization of a polynomial over a finite field .

  4. Integer factorization records - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization_records

    Integer factorization is the process of determining which prime numbers divide a given positive integer.Doing this quickly has applications in cryptography.The difficulty depends on both the size and form of the number and its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, most numbers that have no small factors).

  5. Shor's algorithm - Wikipedia

    en.wikipedia.org/wiki/Shor's_algorithm

    As far as is known, this is not possible using classical (non-quantum) computers; no classical algorithm is known that can factor integers in polynomial time. However, Shor's algorithm shows that factoring integers is efficient on an ideal quantum computer, so it may be feasible to defeat RSA by constructing a large quantum computer.

  6. Rational root theorem - Wikipedia

    en.wikipedia.org/wiki/Rational_root_theorem

    Now any rational root p/q corresponds to a factor of degree 1 in Q[X] of the polynomial, and its primitive representative is then qx − p, assuming that p and q are coprime. But any multiple in Z [ X ] of qx − p has leading term divisible by q and constant term divisible by p , which proves the statement.

  7. Can dogs have eggs? Whether the breakfast food is good for ...

    www.aol.com/lifestyle/dogs-eggs-whether...

    Dogs can eat some "human foods," but it's hard to keep track of what your pet can and cannot consume. Know your dog can have eggs.

  8. ‘I Swapped Walks For Indoor Walking Workouts And Found An ...

    www.aol.com/swapped-walks-indoor-walking...

    Incorporate free weights for any strength exercises included in your chosen indoor walking workout Indoor walking workout modifications: 4 ways to make them easier Reduce the pace and go at your ...

  9. Today's Wordle Hint, Answer for #1251 on Thursday, November ...

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

    SPOILERS BELOW—do not scroll any further if you don't want the answer revealed. The New York Times. Today's Wordle Answer for #1251 on Thursday, November 21, 2024.

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