## Consecutive Product Square

#### Problem

We can see that 3 4 5 6 = 360 = 19^{2}1.

Prove that the product of four consecutive integers is always one less than a perfect square.

Problem ID: 184 (01 Nov 2004) Difficulty: 3 Star

We can see that 3 4 5 6 = 360 = 19^{2}1.

Prove that the product of four consecutive integers is always one less than a perfect square.

Problem ID: 184 (01 Nov 2004) Difficulty: 3 Star