check if moduli are pairwise coprime

cmd/crt.go

@@ -27,12 +27,14 @@ import (
 var remainders []string
 var moduli []string
 
-func solveTwo(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
+func crtSolve(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
+	// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
 	m1 := new(big.Int)
 	m2 := new(big.Int)
 	tmp := new(big.Int)
 	tmp.GCD(m1, m2, n1, n2)
 
+	// x = a1*m2*n2 + a2*m1*n1
 	x := new(big.Int).Set(a1)
 	x.Mul(x, m2)
 	x.Mul(x, n2)
@@ -51,28 +53,50 @@ func solveTwo(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
 	return x, N
 }
 
+func arePairwiseCoprime(moduli []*big.Int) bool {
+	z := new(big.Int)
+	for i, a := range moduli {
+		for _, b := range moduli[i+1:] {
+			z.GCD(nil, nil, a, b)
+			if z.Cmp(big.NewInt(1)) != 0 {
+				return false
+			}
+		}
+	}
+
+	return true
+}
+
 func crt(cmd *cobra.Command, args []string) {
 	if len(remainders) != len(moduli) {
 		log.Fatal("number of remainders and moduli do not match")
 	}
 
-	// TODO: check for pairwise comprime
+	ns := make([]*big.Int, len(moduli))
-
+	for i := range moduli {
-	n1 := new(big.Int)
+		n, ok := new(big.Int).SetString(moduli[i], 10)
-	a1 := new(big.Int)
-	for i := range remainders {
-		n2, ok := new(big.Int).SetString(moduli[i], 10)
 		if !ok {
 			log.Fatal("invalid input " + moduli[i])
 		}
 
+		ns[i] = new(big.Int).Set(n)
+	}
+
+	// TODO: support non-pairwise coprime moduli
+	if !arePairwiseCoprime(ns) {
+		log.Fatalf("moduli %v are not pairwise coprime", moduli)
+	}
+
+	n1 := new(big.Int)
+	a1 := new(big.Int)
+	for i, n2 := range ns {
 		a2, ok := new(big.Int).SetString(remainders[i], 10)
 		if !ok {
 			log.Fatal("invalid input " + remainders[i])
 		}
 
 		if i != 0 {
-			x, N := solveTwo(a1, n1, a2, n2)
+			x, N := crtSolve(a1, n1, a2, n2)
 			n1.Set(N)
 			a1.Set(x)
 		} else {