modular arithmetic

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Related to Congruence class: Modulo arithmetic

modular arithmetic

(mathematics)
(Or "clock arithmetic") A kind of integer arithmetic that reduces all numbers to one of a fixed set [0..N-1] (this would be "modulo N arithmetic") by effectively repeatedly adding or subtracting N (the "modulus") until the result is within this range.

The original mathematical usage considers only __equivalence__ modulo N. The numbers being compared can take any values, what matters is whether they differ by a multiple of N. Computing usage however, considers modulo to be an operator that returns the remainder after integer division of its first argument by its second.

Ordinary "clock arithmetic" is like modular arithmetic except that the range is [1..12] whereas modulo 12 would be [0..11].
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Let A mod M be a congruence class containing a squarefree integer, and suppose that A mod M is not entirely contained in the residue class 7 mod 8.
Then [a]D = [b]D and so by the property of congruence class, we obtain a * b [member of] D and b * a [member of] D.
n], the congruence class of x mod [THETA] is denoted by [[x].
infinity]]] that identifies the representative of a congruence class.
We prove the existence of a unique factorization of a contextual trace as a product of images, in the canonical morphism [phi], of words related to the Lukasiewicz words and characterize the lexicographically minimum and maximum representatives of a congruence class.
For each congruence class C, let [union]C denote the union of the regions in C.
alpha]] is a semilattice congruence class of S and so b [member of] [S.

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