Question 24
Observe that
$$\begin{aligned}1\times2\times3\times4+1&=5^2,\\2\times3\times4\times5+1&=11^2,\\3\times4\times5\times6+1&=19^2.\end{aligned}$$
Prove that the product of four consecutive positive integers, increased by one, is a perfect square.
$$\begin{aligned}1\times2\times3\times4+1&=5^2,\\2\times3\times4\times5+1&=11^2,\\3\times4\times5\times6+1&=19^2.\end{aligned}$$
Prove that the product of four consecutive positive integers, increased by one, is a perfect square.