Question

Adding K to the product of four consecutive odd numbers, the sum will be a perfect square number. What is the value of K?​

Answer 1

Answer:

Let x be the average of these numbers. The numbers are (x-3), (x-1), (x+1), (x+3).

Product = (x-3)(x+3)(x-1)(x+1) = (x²-9) (x²-1).

Substitute n = (x²-5).

Product = (n-4)(n+4) = (n²-16) = (x²-5)² -16.

Adding 16 to the product always yields a square number ⇒ K=16.