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  2. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...

  3. Frobenius theorem (real division algebras) - Wikipedia

    en.wikipedia.org/wiki/Frobenius_theorem_(real...

    Proof of Claim: Pick a in D with characteristic polynomial p(x). By the fundamental theorem of algebra, we can write By the fundamental theorem of algebra, we can write

  4. 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.

  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. Division lattice - Wikipedia

    en.wikipedia.org/wiki/Division_lattice

    The non-negative integers partially ordered by divisibility. The division lattice is an infinite complete bounded distributive lattice whose elements are the natural numbers ordered by divisibility. Its least element is 1, which divides all natural numbers, while its greatest element is 0, which is divisible by all natural numbers.

  7. 10 of the Most Expensive Fines in Football - AOL

    www.aol.com/10-most-expensive-fines-football...

    NFL players have sky-high salaries and contracts that would make the average person feel faint. They also get slapped with fines left and right, some frivolous and some substantial.

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