Try to prove that the product of four continuous positive integers plus 1 must be a complete square? (write the proof and steps)

Try to prove that the product of four continuous positive integers plus 1 must be a complete square? (write the proof and steps)

You can set these four numbers as N, (n + 1), (n + 2), (n + 3) n (n + 1) (n + 2) (n + 3) + 1 = (n ^ 2 + 3n) (n ^ 2 + 3N + 2) + 1 = (n ^ 2 + 3n) ^ 2 + 2 (n ^ 2 + 3n) + 1 = (n ^ 2 + 3N + 1) ^ 2