This problem from Colin Hughes at *Maths Challenge* is a most surprising result that takes a bit of tinkering to solve.

“**Problem**

We can see that 3 x 4 x 5 x 6 = 360 = 19² – 1. Prove that the product of four consecutive integers is always one less than a perfect square.”

The result is so mysterious at first that you begin to understand why the ancient Pythagoreans had a mystical relationship with mathematics.

See the Consecutive Product Square.

(**Update 11/12/2020**) **Generalization and Visual Proof ** Continue reading