Help proving the product of any four consecutive integers is one less than a perfect square Apparently this is a true statement, but I cannot figure out how to prove this. I have tried setting 
$$(m)(m + 1)(m + 2)(m + 3) = (m + 4)^2 - 1 $$
but to no avail. Could someone point me in the right direction? 

If you have trouble approaching this, try some examples: Note that (for instance)
$$
1 \times \color{red}{2 \times 3} \times 4 = 24 = 5^2-1
$$
$$
2 \times \color{red}{3 \times 4} \times 5 = 120 = 11^2-1
$$
$$
3 \times \color{red}{4 \times 5} \times 6 = 360 = 19^2-1
$$
and observe that
$$
5 = \color{red}{2 \times 3} - 1
$$
$$
11 = \color{red}{3 \times 4} - 1
$$
$$
19 = \color{red}{4 \times 5} - 1
$$
So try seeing if
$$
m\color{red}{(m+1)(m+2)}(m+3) = [\color{red}{(m+1)(m+2)}-1]^2-1
$$
