# modular arithmetic

## noun

: arithmetic that deals with whole numbers where the numbers are replaced by their remainders after division by a fixed number
in a modular arithmetic with modulus 5, 3 multiplied by 4 is 2

## Examples of modular arithmetic in a Sentence

Recent Examples on the Web Suddenly, mathematicians learned to apply tools like modular arithmetic and factorization to these new number systems. Quanta Magazine, 1 Nov. 2023 Using this complicated modular arithmetic based on a prime number, but essentially raising a number to hidden powers as in the previous section, Alice and Bob establish a common secret number, in this example, 3. Amir Aczel, Discover Magazine, 31 July 2013 There are two good reasons for using modular arithmetic. Amir Aczel, Discover Magazine, 31 July 2013 Mathematicians employ modular arithmetic all the time to investigate the deepest questions in their field. Quanta Magazine, 14 Sep. 2021 The Chinese remainder theorem resides in a field of math called modular arithmetic that studies numbers by analyzing their remainders when they are divided by other numbers. Quanta Magazine, 18 Nov. 2021 In other cases, modular arithmetic can rule out the possibility that a polynomial equation has any whole-number solutions. Quanta Magazine, 14 Sep. 2021 To see how p-adic number systems emerge from modular arithmetic, start by classifying all integers modulo a specific prime number. Quanta Magazine, 19 Oct. 2020 The p-adic numbers are based in modular arithmetic, which is a method of counting that loops back on itself, like a clock. Quanta Magazine, 19 Oct. 2020

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'modular arithmetic.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

First Known Use

1941, in the meaning defined above

Time Traveler
The first known use of modular arithmetic was in 1941

## Dictionary Entries Near modular arithmetic

modular arithmetic

## Cite this Entry

“Modular arithmetic.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/modular%20arithmetic. Accessed 13 Jun. 2024.

## Kids Definition

modular arithmetic

noun
: arithmetic that deals with whole numbers in such a way that all numbers are replaced by their remainders after division by a modulus
5 hours after 10 o'clock is 3 o'clock because clocks follow a modular arithmetic with modulus 12

## More from Merriam-Webster on modular arithmetic

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