Let \(a, b, c, d\) be four consecutive integers. Prove that \(abcd + 1\) is a perfect square. Furthermore, prove that the the square root of \(abcd + 1\) is equal to the average of \(ad\) and \(bc\).
Let be represented as .
Factoring yields , proving that it is a perfect square.
The average of and is
which is the square-root of .
Check out my other notes at Proof, Disproof, and Derivation