Problem
ALG-B1-M10-P003 Three neighboring integers
#3
★☆☆☆☆ Level 1 of 5
Prove that \(n(n+1)(n+2)\) is divisible by \(6\) for every integer \(n\).
Among three consecutive integers there is a multiple of \(3\) and an even number.
Among three consecutive integers, one is divisible by \(3\), and one by \(2\). Therefore the product is divisible by \(2\cdot3=6\).
Divisibility through product structure.