Let $ \{X_n\}$ and $ \{Y_n\}$ denote two sequences of integers defined as follows: \[ X_0 = 1,\ X_1 = 1,\ X_{n + 1} = X_n + 2X_{n - 1} \quad (n = 1,2,3,\ldots), \\ Y_0 = 1,\ Y_1 = 7,\ Y_{n + 1} = 2Y_n + 3Y_{n - 1} \quad (n = 1,2,3,\ldots).\] Prove that, except for the "1", there is no term which occurs in both sequences.