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