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2. Divisibility rule - Wikipedia

   en.wikipedia.org/wiki/Divisibility_rule

   We also have the rule that 10 x + y is divisible iff x + 4 y is divisible by 13. For example, to test the divisibility of 1761 by 13 we can reduce this to the divisibility of 461 by the first rule. Using the second rule, this reduces to the divisibility of 50, and doing that again yields 5. So, 1761 is not divisible by 13.

3. Divisibility (ring theory) - Wikipedia

   en.wikipedia.org/wiki/Divisibility_(ring_theory)

   Let R be a ring, [a] and let a and b be elements of R.If there exists an element x in R with ax = b, one says that a is a left divisor of b and that b is a right multiple of a. [1] ...

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. 1001 (number) - Wikipedia

   en.wikipedia.org/wiki/1001_(number)

   Two properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are 1001 = 7 × 11 × 13 in prime factors 10 3 ≡ -1 (mod 1001) The method simultaneously tests for divisibility by any of the factors ...

6. 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 ...

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