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  2. Coprime integers - Wikipedia

    en.wikipedia.org/wiki/Coprime_integers

    For example, the integers 6, 10, 15 are coprime because 1 is the only positive integer that divides all of them. If every pair in a set of integers is coprime, then the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger condition than setwise ...

  3. Bunyakovsky conjecture - Wikipedia

    en.wikipedia.org/wiki/Bunyakovsky_conjecture

    A seemingly weaker yet equivalent statement to Bunyakovsky's conjecture is that for every integer polynomial () that satisfies (1)–(3), () is prime for at least one positive integer : but then, since the translated polynomial (+) still satisfies (1)–(3), in view of the weaker statement () is prime for at least one positive integer >, so ...

  4. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    It is convenient at this point (per Trautman 1998) to call a triple (a,b,c) standard if c > 0 and either (a,b,c) are relatively prime or (a/2,b/2,c/2) are relatively prime with a/2 odd. If the spinor [m n] T has relatively prime entries, then the associated triple (a,b,c) determined by is a standard triple. It follows that the action of the ...

  5. Primal ideal - Wikipedia

    en.wikipedia.org/wiki/Primal_ideal

    In mathematics, an element a of a commutative ring R is called (relatively) prime to an ideal I if whenever ab is an element of I then b is also an element of I. A proper ideal I of a commutative ring A is said to be primal if the elements that are not prime to it form an ideal.

  6. Prime (symbol) - Wikipedia

    en.wikipedia.org/wiki/Prime_(symbol)

    The prime symbol ′ is commonly used to represent feet (ft), and the double prime ″ is used to represent inches (in). [2] The triple prime ‴, as used in watchmaking, represents a ligne (1 ⁄ 12 of a "French" inch, or pouce, about 2.26 millimetres or 0.089 inches).

  7. Residue number system - Wikipedia

    en.wikipedia.org/wiki/Residue_number_system

    A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.

  8. Disjoint sets - Wikipedia

    en.wikipedia.org/wiki/Disjoint_sets

    According to one such definition, the family is disjoint if each two sets in the family are either identical or disjoint. This definition would allow pairwise disjoint families of sets to have repeated copies of the same set. According to an alternative definition, each two sets in the family must be disjoint; repeated copies are not allowed.

  9. Schur's theorem - Wikipedia

    en.wikipedia.org/wiki/Schur's_theorem

    This consequence of the theorem can be recast in a familiar context considering the problem of changing an amount using a set of coins. If the denominations of the coins are relatively prime numbers (such as 2 and 5) then any sufficiently large amount can be changed using only these coins. (See Coin problem.)