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What is the remainder when we divide $19^{2021}$ by $4$? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Congruence
We note that $19^{2} \equiv 1$ $( \text{mod} \textbackslash; 4)$ and hence:  $19^{2021} \equiv 1^{1010} \times 3 \equiv 3$ $( \text{mod} \textbackslash; 3)$ 