Problem
NT-B1-M03-P011 Product of Consecutive Numbers
#11
★★☆☆☆ Level 2 of 5
Use congruences to prove that \(n^2+n\) is even for every integer \(n\).
Check residues of \(n\) modulo \(2\).
If \(n\equiv0\pmod2\), then \(n^2+n\equiv0\). If \(n\equiv1\pmod2\), then \(n^2+n\equiv1+1\equiv0\pmod2\). Thus the expression is always even.
Shows parity as a special case of modular reasoning.