implement -t flag

cmd/primitiveRoot.go

@@ -73,8 +73,44 @@ func computeNaive(modulus *big.Int) (*big.Int, error) {
 	return nil, errors.New("no primitive root")
 }
 
-func computeFromFactors(modulus *big.Int, tpf []string) *big.Int {
+func computeFromFactors(modulus *big.Int, tpf []string) (*big.Int, error) {
-	return nil
+	phi := big.NewInt(1)
+	factors := make(map[string]bool)
+	for _, s := range tpf {
+		p, ok := new(big.Int).SetString(s, 10)
+		if !ok {
+			return nil, errors.New("invalid input " + s)
+		}
+
+		phi.Mul(phi, p)
+		factors[p.Text(10)] = true
+	}
+
+	for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
+		gcd := new(big.Int).GCD(nil, nil, g, modulus)
+		if gcd.Cmp(big.NewInt(1)) != 0 {
+			continue
+		}
+
+		isPrimitive := true
+		for p := range factors {
+			e := new(big.Int)
+			f, _ := new(big.Int).SetString(p, 10)
+			k := new(big.Int).Div(phi, f)
+			e.Exp(g, k, modulus)
+
+			if e.Cmp(big.NewInt(1)) == 0 {
+				isPrimitive = false
+				break
+			}
+		}
+
+		if isPrimitive {
+			return g, nil
+		}
+	}
+
+	return nil, errors.New("no primitive root")
 }
 
 func primitiveRoot(cmd *cobra.Command, args []string) {
@@ -91,7 +127,10 @@ func primitiveRoot(cmd *cobra.Command, args []string) {
 			log.Fatal(err)
 		}
 	} else {
-		root = computeFromFactors(m, tpf)
+		root, err = computeFromFactors(m, tpf)
+		if err != nil {
+			log.Fatal(err)
+		}
 	}
 
 	fmt.Println(root)