add more help text

cmd/jacobi.go

@@ -51,8 +51,16 @@ func jacobi(cmd *cobra.Command, args []string) {
 var jacobiCmd = &cobra.Command{
 	Use:   "jacobi -a A -n N",
 	Short: "Compute the Jacobi symbol",
-	Long:  `Compute the Jacobi symbol (a | n).`,
-	Run:   jacobi,
+	Long: `Compute the Jacobi symbol (a | n).
+
+The Jacobi symbol is useful for studying quadratic residues. a is a quadratic residue modulo n if there exists a value x such that
+x^2 = a (mod n)
+
+If a is a quadratic residue modulo n and gcd(a, n) = 1, then (a | n) = 1.
+If (a | n) = -1, then a is a quadratic nonresidue modulo n.
+
+However, (a | n) = 1 does not guarantee that a is a quadratic residue modulo n.`,
+	Run: jacobi,
 }
 
 func init() {