Problem
NT-B2-M02-P005 Last Digit of a Square
#5
★★☆☆☆ Level 2 of 5
Prove that a square of an integer cannot end in \(2\), \(3\), \(7\), or \(8\).
Work modulo \(10\).
It is enough to check residues \(0,1,\ldots,9\). Their squares modulo \(10\) are \(0,1,4,9,6,5,6,9,4,1\). The residues \(2,3,7,8\) do not appear.
It looks elementary, but it trains a full residue-set argument.