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Modulus

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For $ a>0$ and $ x\in\mathbb{R}$ the remainder obtained when dividing $ x$ by $ a$ is denoted by $ x\,\operatorname{mod}\,a$, that is,

$\displaystyle x\,\operatorname{mod}\,a := x - n a \in [0,a) $

where $ n$ is an integer. If

$\displaystyle x\,\operatorname{mod}\,a = y\,\operatorname{mod}\,a\, , $

then $ x$ and $ y$ are said to be congruent modulo $ a$.

see also:

  automatically generated 3/31/2005