How does the Modular Arithmetic work?

a mod m = remainder of a ÷ m Then: (a+b) mod m = ((a mod m)+(b mod m)) mod m Then: Modular exponentiation: fast algorithm for aⁿ mod m.

Can you give an example of how to use the Modular Arithmetic?

Example: Input 17 mod 5 gives a result of 2 (17 = 3×5 + 2).

Is the Modular Arithmetic free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Modular Arithmetic?

Our Modular Arithmetic uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Modular Arithmetic

Modulo operations and modular exponentiation

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modulus m

Modular arithmetic wraps numbers around after reaching a modulus. a mod m is the remainder when a is divided by m. Foundational in cryptography, checksums, and number theory.

1a mod m = remainder of a ÷ m
2(a+b) mod m = ((a mod m)+(b mod m)) mod m
3Modular exponentiation: fast algorithm for aⁿ mod m

17 mod 5=217 = 3×5 + 2

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Fun Fact

RSA encryption (securing all HTTPS traffic) relies on modular exponentiation. Reversing the operation (discrete logarithm) is computationally infeasible for large numbers.

References

▸Modular arithmetic — Wikipedia

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Modular Arithmetic

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