A-M baby

Task/Multiplicative-order/Haskell/multiplicative-order-1.hs

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+primeFacsExp :: Integer -> [(Integer, Int)]

Task/Multiplicative-order/Haskell/multiplicative-order-2.hs

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+powerMod :: (Integral a, Integral b) => a -> a -> b -> a
+powerMod m _ 0 =  1
+powerMod m x n | n > 0 = f x' (n-1) x' where
+  x' = x `rem` m
+  f _ 0 y = y
+  f a d y = g a d where
+    g b i | even i    = g (b*b `rem` m) (i `quot` 2)
+          | otherwise = f b (i-1) (b*y `rem` m)
+powerMod m _ _  = error "powerMod: negative exponent"

Task/Multiplicative-order/Haskell/multiplicative-order-3.hs

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+multOrder a m
+  | gcd a m /= 1  = error "Arguments not coprime"
+  | otherwise     = foldl1' lcm $ map (multOrder' a) $ primeFacsExp m
+
+multOrder' a (p,k) = r where
+  pk = p^k
+  t = (p-1)*p^(k-1) -- totient \Phi(p^k)
+  r = product $ map find_qd $ primeFacsExp $ t
+  find_qd (q,e) = q^d where
+    x = powerMod pk a (t `div` (q^e))
+    d = length $ takeWhile (/= 1) $ iterate (\y -> powerMod pk y q) x