Problem
NT-B1-M01-P007 Four Consecutive Integers
#7
★★☆☆☆ Level 2 of 5
Prove that \(24\mid n(n+1)(n+2)(n+3)\) for every integer \(n\).
You need to collect the factors \(3\) and \(8\).
Among four consecutive integers, one is divisible by \(3\). Also, there are two even numbers, one of which is divisible by \(4\). These two even numbers together give a factor \(8\). Therefore the product is divisible by \(8\cdot3=24\).
Watch that the student proves divisibility by \(8\), not only by \(4\).