SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Mathematica > Mathematics and Algorithms > Number Theory >

PowerMod

PowerMod[a, b, m]
gives a^b mod m.

PowerMod[a, -1, m]
finds the modular inverse of a modulo m.

PowerMod[a, 1/r, m]
finds the smallest modular root of a.

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

For positive b, PowerMod[a, b, m] gives the same result as Mod[a^b, m] but is much more efficient.

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

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 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: