my $m = 15;                             # max digit
for my $r ( 0 .. $m ) {                 # remainder
    print "$r:\t";
    for my $w ( 2 .. $m ) {             # witness
        if ( $r == ( $r * $w ) % $m ) {
            print "$w "
        }
    }
    print "\n"
}

# 0:      2 3 4 5 6 7 8 9 10 11 12 13 14 15
# 1:
# 2:
# 3:      6 11
# 4:
# 5:      4 7 10 13
# 6:      6 11
# 7:
# 8:
# 9:      6 11
# 10:     4 7 10 13
# 11:
# 12:     6 11
# 13:
# 14:
# 15: