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  2. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    To test the divisibility of a number by a power of 2 or a power of 5 (2 n or 5 n, in which n is a positive integer), one only need to look at the last n digits of that number. To test divisibility by any number expressed as the product of prime factors p 1 n p 2 m p 3 q {\displaystyle p_{1}^{n}p_{2}^{m}p_{3}^{q}} , we can separately test for ...

  3. Trial division - Wikipedia

    en.wikipedia.org/wiki/Trial_division

    Given an integer n (n refers to "the integer to be factored"), the trial division consists of systematically testing whether n is divisible by any smaller number. Clearly, it is only worthwhile to test candidate factors less than n, and in order from two upwards because an arbitrary n is more likely to be divisible by two than by three, and so on.

  4. Primality test - Wikipedia

    en.wikipedia.org/wiki/Primality_test

    The first deterministic primality test significantly faster than the naive methods was the cyclotomy test; its runtime can be proven to be O((log n) c log log log n), where n is the number to test for primality and c is a constant independent of n. Many further improvements were made, but none could be proven to have polynomial running time.

  5. Euclid's lemma - Wikipedia

    en.wikipedia.org/wiki/Euclid's_lemma

    The two first subsections, are proofs of the generalized version of Euclid's lemma, namely that: if n divides ab and is coprime with a then it divides b. The original Euclid's lemma follows immediately, since, if n is prime then it divides a or does not divide a in which case it is coprime with a so per the generalized version it divides b.

  6. Euclid's theorem - Wikipedia

    en.wikipedia.org/wiki/Euclid's_theorem

    Several variations on Euclid's proof exist, including the following: The factorial n! of a positive integer n is divisible by every integer from 2 to n, as it is the product of all of them.

  7. Zsigmondy's theorem - Wikipedia

    en.wikipedia.org/wiki/Zsigmondy's_theorem

    In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if > > are coprime integers, then for any integer , there is a prime number p (called a primitive prime divisor) that divides and does not divide for any positive integer <, with the following exceptions:

  8. Today's Wordle Hint, Answer for #1260 on Saturday, November ...

    www.aol.com/todays-wordle-hint-answer-1260...

    If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1260 ahead. Let's start with a few hints.

  9. Eisenstein's criterion - Wikipedia

    en.wikipedia.org/wiki/Eisenstein's_criterion

    Consider the polynomial Q(x) = 3x 4 + 15x 2 + 10.In order for Eisenstein's criterion to apply for a prime number p it must divide both non-leading coefficients 15 and 10, which means only p = 5 could work, and indeed it does since 5 does not divide the leading coefficient 3, and its square 25 does not divide the constant coefficient 10.