Problem
ALG-B1-M09-P001 Product of two neighboring integers
#1
★☆☆☆☆ Level 1 of 5
Prove that \(n^2-n\) is divisible by \(2\) for every integer \(n\).
Factor \(n^2-n\).
\(n^2-n=n(n-1)\). This is the product of two consecutive integers, one of which is even. Hence the product is divisible by \(2\).
Basic divisibility through consecutive integers.