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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. Goldbach's conjecture - Wikipedia

   en.wikipedia.org/wiki/Goldbach's_conjecture

   Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.It states that every even natural number greater than 2 is the sum of two prime numbers.

4. 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.

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. Divisibility test - Wikipedia

   en.wikipedia.org/?title=Divisibility_test&...

   Pages for logged out editors learn more. Contributions; Talk; Divisibility test

7. Number theory - Wikipedia

   en.wikipedia.org/wiki/Number_theory

   Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."