## Residue multiplication table

echo "mulres version 0.1 (c) Brian Chandler 1993\n";
echo "Syntax: mulres n\n\
This prints the multiplication table of the residues modulo n which\n\
are coprime to n. (In other words, multiplication round the \"number\n\
circle of size n\" in place of the ordinary \"number line\" of integers.)\n\
\n\
The function phi(n) is defined as the number of these residues.\n\
Moreover, the residues form a group under multiplication, as you\n\
can check from the table: associativity is obvious, since \n\
multiplication in the integers is associative, multiplication is\n\
closed, since if you multiply together two numbers coprime to n,\n\
the answer must also be coprime, and um inverses are established \n\
by a bit of hand waving (the cancellation laws work, for a start).\n\n";

coprime: argument must be number

coprime: argument must be positive

Modulus:

Group of coprime residues modulo under multiplication