michael@0: # This Source Code Form is subject to the terms of the Mozilla Public
michael@0: # License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0: # file, You can obtain one at http://mozilla.org/MPL/2.0/.
michael@0: 
michael@0: =head1 NAME
michael@0: 
michael@0:  lap - compute least annihilating power of a number
michael@0: 
michael@0: =head1 SYNOPSIS
michael@0: 
michael@0:  lap <a> <m>
michael@0: 
michael@0: =head1 DESCRIPTION
michael@0: 
michael@0: The B<lap> program computes the order of I<a> modulo I<m>, for
michael@0: arbitrary precision integers I<a> and I<m>.  The B<order> of I<a>
michael@0: modulo I<m> is defined as the smallest positive value I<n> for which
michael@0: I<a> raised to the I<n>th power, modulo I<m>, is equal to 1.  The
michael@0: order may not exist, if I<m> is composite.
michael@0: 
michael@0: =head1 RESTRICTIONS
michael@0: 
michael@0: This program is very slow, especially for large moduli.  It is
michael@0: intended as a way to help find primitive elements in a modular field,
michael@0: but it does not do so in a particularly inefficient manner.  It was
michael@0: written simply to help verify that a particular candidate does not
michael@0: have an obviously short cycle mod I<m>.
michael@0: 
michael@0: =head1 SEE ALSO
michael@0: 
michael@0: gcd(1), invmod(1), isprime(1)
michael@0: 
michael@0: =head1 AUTHOR
michael@0: 
michael@0:  Michael J. Fromberger <sting@linguist.dartmouth.edu>
michael@0:  Thayer School of Engineering, Hanover, New Hampshire, USA