Always Perfect

2 x 3 x 4 x 5 + 1 = 11 x 11

21 x 22 x 23 x 24 + 1 = 505 x 505

Pick your own four consecutive numbers, find their product and add one. Is your answer a perfect square?

Show that if you add 1 to the product of  any four consecutive numbers the answer is ALWAYS a perfect square.

Click here to download the ALWAYS PERFECT worksheet.

Click to download Notes for Teachers: English version and French version.

This problem is adapted from the NRICH task Always Perfect with permission of the University of Cambridge. All rights reserved.