update

Task/Multiplicative-order/Perl-6/multiplicative-order.pl6

@@ -0,0 +1,51 @@
+my @primes := 2, grep *.is-prime, (3,5,7...*);
+
+sub factor($a is copy) {
+    gather {
+        for @primes -> $p {
+            my $j = 0;
+            while $a %% $p {
+                $a div= $p;
+                $j++;
+            }
+            take $p => $j if $j > 0;
+            last if $a < $p * $p;
+        }
+
+        take $a => 1 if $a > 1;
+    }
+}
+
+sub mo-prime($a, $p, $e) {
+    my $m = $p ** $e;
+    my $t = ($p - 1) * ($p ** ($e - 1)); #  = Phi($p**$e) where $p prime
+    my @qs = 1;
+    for factor($t) -> $f {
+        @qs = @qs.map(-> $q { (0..$f.value).map(-> $j { $q * $f.key ** $j }) });
+    }
+    @qs.sort();
+
+    @qs.first(-> $q { expmod( $a, $q, $m ) == 1});
+}
+
+sub mo($a, $m) {
+    $a gcd $m == 1 || die "$a and $m are not relatively prime";
+    [lcm] 1, factor($m).map(-> $r { mo-prime($a, $r.key, $r.value) });
+}
+
+sub MAIN("test") {
+    use Test;
+
+    for (10, 21, 25, 150, 1231, 123141, 34131) -> $n {
+        # say factor($n).perl;
+        # say factor($n).map(-> $pair { $pair.key ** $pair.value }).perl;
+        is ([*] factor($n).map(-> $pair { $pair.key ** $pair.value })), $n, "$n factors correctly";
+    }
+
+    is mo(37, 1000), 100, 'mo(37,1000) == 100';
+    my $b = 10**20-1;
+    is mo(2, $b), 3748806900, 'mo(2,10**20-1) == 3748806900';
+    is mo(17, $b), 1499522760, 'mo(17,10**20-1) == 1499522760';
+    $b = 100001;
+    is mo(54, $b), 9090, 'mo(54,100001) == 9090';
+}

Task/Multiplicative-order/Racket/multiplicative-order-1.rkt

@@ -0,0 +1,25 @@
+#lang racket
+(require math)
+
+(define (order a n)
+  (unless (coprime? a n) (error 'order "arguments must be coprime"))
+  (for/fold ([o 1]) ([r (factorize n)])
+    (lcm o (order1 a r))))
+
+(define (order1 a p&e)
+  (match-define (list p e) p&e)
+  (define m (expt p e))
+  (define t (* (- p 1) (expt p (- e 1))))
+  (define qs
+    (for/fold ([qs '(1)]) ([f (factorize t)])
+       (match f [(list f0 f1)
+                 (for*/list ([q qs] [j (in-range (+ 1 f1))])
+                   (* q (expt f0 j)))])))
+  (for/or ([q (sort qs <)] #:when (= (modular-expt a q m) 1)) q))
+
+
+(order 37 1000)
+(order (+ (expt 10 100) 1) 7919)
+(order (+ (expt 10 1000) 1) 15485863)
+(order (- (expt 10 10000) 1) 22801763489)
+(order 13 (+ 1 (expt 10 80)))

Task/Multiplicative-order/Racket/multiplicative-order-2.rkt

@@ -0,0 +1,5 @@
+100
+3959
+15485862
+22801763488
+109609547199756140150989321269669269476675495992554276140800