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  2. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...

  3. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.

  4. Modular equation - Wikipedia

    en.wikipedia.org/wiki/Modular_equation

    Modular equation. In mathematics, a modular equation is an algebraic equation satisfied by moduli, [1] in the sense of moduli problems. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli. The most frequent use of the term modular equation is in ...

  5. Absolute value - Wikipedia

    en.wikipedia.org/wiki/Absolute_value

    The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...

  6. Modulo (mathematics) - Wikipedia

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

    Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.

  7. Montgomery modular multiplication - Wikipedia

    en.wikipedia.org/wiki/Montgomery_modular...

    For computational purposes it is also necessary that division and reduction modulo R are inexpensive, and the modulus is not useful for modular multiplication unless R > N. The Montgomery form of the residue class a with respect to R is aR mod N, that is, it is the representative of the residue class aR. For example, suppose that N = 17 and ...

  8. Modulus (algebraic number theory) - Wikipedia

    en.wikipedia.org/wiki/Modulus_(algebraic_number...

    Modulus (algebraic number theory) In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, [1] or extended ideal[2]) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.

  9. Norm (mathematics) - Wikipedia

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

    Norm (mathematics) In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space ...

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