# modular arithmetic

## modular arithmetic

noun
arithmetic in which numbers that are congruent modulo a given number are treated as the same. Compare congruence ( def 2 ), modulo, modulus ( def 2b ).

Origin:
1955–60

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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Computing Dictionary

### modular arithmetic definition

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].
(2003-03-28)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Encyclopedia Britannica
Encyclopedia

modular arithmetic

in its most elementary form, arithmetic done with a count that resets itself to zero every time a certain whole number N greater than one, known as the modulus (mod), has been reached. Examples are a digital clock in the 24-hour system, which resets itself to 0 at midnight (N = 24), and a circular protractor marked in 360 degrees (N = 360). Modular arithmetic is important in number theory, where it is a fundamental tool in the solution of Diophantine equations (particularly those restricted to integer solutions). Generalizations of the subject led to important 19th-century attempts to prove Fermat's last theorem and the development of significant parts of modern algebra.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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Example sentences
Eg, you could teach modular arithmetic and then immediately show the power of
this method.
Explains simple encoding and decoding of messages for student learning of
modular arithmetic.
There are also exercises leading to the concept of place value and work with
modular arithmetic.
Students explore the properties of clock arithmetic or a modular arithmetic
system.