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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. 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.

5. Parity (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Parity_(mathematics)

   The following laws can be verified using the properties of divisibility. They are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic ...

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. NYT ‘Connections’ Hints and Answers Today, Thursday, December 12

   www.aol.com/nyt-connections-hints-answers-today...

   If you've been having trouble with any of the connections or words in Thursday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down