Problem
NT-B1-M11-P013 Residues of an Expression
#13
★★★☆☆ Level 3 of 5
Find all residues \(n\pmod7\) for which \(7\mid n^2+n+1\).
Check the seven residues.
For \(n=0,1,2,3,4,5,6\), the expression \(n^2+n+1\) gives residues \(1,3,0,6,0,3,1\). Hence \(n\equiv2\) or \(4\pmod7\).
Trains careful residue tables.