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  2. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as: [2] [5] Parentheses; Exponentiation; Multiplication and division; Addition and subtraction

  3. Operation (mathematics) - Wikipedia

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

    In mathematics, an operation is a function from a set to itself. For example, an operation on real numbers will take in real numbers and return a real number. An operation can take zero or more input values (also called "operands" or "arguments") to a well-defined output value.

  4. Montgomery modular multiplication - Wikipedia

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

    Classical modular multiplication reduces the double-width product ab using division by N and keeping only the remainder. This division requires quotient digit estimation and correction. The Montgomery form, in contrast, depends on a constant R > N which is coprime to N, and the only division necessary in Montgomery multiplication is division by R.

  5. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Order preservation Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]

  6. Multiplicative order - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_order

    If the order of a is actually equal to φ(n), and therefore as large as possible, then a is called a primitive root modulo n. This means that the group U(n) is cyclic and the residue class of a generates it. The order of a (mod n) also divides λ(n), a value of the Carmichael function, which is an even stronger statement than the divisibility ...

  7. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    On currently available processors, a bit-wise shift instruction is usually (but not always) faster than a multiply instruction and can be used to multiply (shift left) and divide (shift right) by powers of two. Multiplication by a constant and division by a constant can be implemented using a sequence of shifts and adds or subtracts. For ...

  8. Ordinal arithmetic - Wikipedia

    en.wikipedia.org/wiki/Ordinal_arithmetic

    A left division with remainder property holds: for all α and β, if β > 0, then there are unique γ and δ such that α = β · γ + δ and δ < β. Right division does not work: there is no α such that α · ω ≤ ω ω ≤ (α + 1) · ω. The ordinal numbers form a left near-semiring, but do not form a ring.

  9. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    When multiplication is mentioned in elementary mathematics, it usually refers to this kind of multiplication. From the point of view of algebra, the real numbers form a field, which ensures the validity of the distributive law. First example (mental and written multiplication)

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