Problem
NT-B1-M12-P004 Set 1. Squares Modulo \(3\)
#4
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Which residues can an integer square have modulo \(3\)?
Check \(0,1,2\).
If \(n\equiv0,1,2\pmod3\), then \(n^2\equiv0,1,1\pmod3\). Only \(0\) and \(1\) are possible.
Basis for modular impossibility.