Initial data commit

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