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Task/Multiplicative-order/EchoLisp/multiplicative-order.echolisp

@@ -0,0 +1,32 @@
+(require 'bigint)
+
+;; factor-exp returns a list ((p k) ..) : a = p1^k1 * p2^k2 ..
+(define (factor-exp a)
+	(map (lambda (g) (list (first g) (length g)))
+					(group* (prime-factors a))))
+
+;; copied from Ruby
+(define (_mult_order a p k  (x))
+	(define pk (expt p k))
+	(define t (* (1- p) (expt p (1- k))))
+	(define r 1)
+	(for [((q e) (factor-exp t))]
+	    (set! x (powmod a (/ t (expt q e)) pk))
+	    (while (!= x 1)
+	    	(*= r q)
+	    	(set! x (powmod x q pk))))
+	r)
+	
+(define (order a m)
+        "multiplicative order : (order a m) →  n : a^n = 1 (mod m)"
+	(assert (= 1 (gcd a m)) "a and m must be coprimes")
+	(define mopks (for/list [((p k)  (factor-exp m))] (_mult_order a p k)))
+	(for/fold (n 1) ((mopk mopks)) (lcm n mopk)))
+
+;; results
+order 37 1000)
+   → 100
+(order (+ (expt 10 100) 1) 7919)
+   → 3959
+(order (+ (expt 10 1000) 1) 15485863)
+   → 15485862