Problem
NT-B1-M03-P009 A Square Cannot Have Residue 2 or 3
#9
★★☆☆☆ Level 2 of 5
Prove that no square of an integer has remainder \(2\) or \(3\) upon division by \(4\).
Use the table of squares modulo \(4\).
Every square modulo \(4\) is \(0\) or \(1\). Residues \(2\) and \(3\) do not occur, so a square cannot have these remainders.
Basic negative statement.