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Mathematica > Mathematics and Algorithms > Number Theory > PowerMod >

PowerMod

gives

finds the modular inverse of a modulo m.

finds a modular r

root of a.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

For positive b, PowerMod gives the same result as Mod but is much more efficient.

PowerMod allows negative and rational values of b. It returns unevaluated if the corresponding modular inverse or root does not exist.

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Compute the multiplicative inverse of 3 modulo 7:

Check the result:

PowerMod works with numbers of any size, and does not need to compute the explicit power:

PowerMod automatically threads itself over lists:

Compute the modular square root of 6 modulo 10:

Build an RSA-like toy encryption scheme. Start with the modulus:

Find the universal exponent of the multiplication group modulo n:

Private key:

Public key:

Encrypt a message:

Decrypt it:

Modular square roots may not exist: