# multiplicativeOrder -- multiplicative order of an integer modulo another

## Synopsis

• Usage:
multiplicativeOrder(a, b)
• Inputs:
• a, an integer, whose multiplicative order is to be computed
• b, an integer, prime to a; the modulus
• Outputs:
• an integer, the multiplicative order of a mod b

## Description

multiplicativeOrder(a,b) computes the multiplicative order of $a$ modulo $b$.

 i1 : multiplicativeOrder(2, 11^2) o1 = 110 i2 : multiplicativeOrder(3, 11^2) o2 = 5 i3 : multiplicativeOrder(4, 11^2) o3 = 55

If $a$ and $b$ are not relatively prime, multiplicativeOrder(a, b) returns an error.

## Ways to use multiplicativeOrder :

• "multiplicativeOrder(ZZ,ZZ)"

## For the programmer

The object multiplicativeOrder is .