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number theory intermediate
Problem
What is Express your answer in base 3.
Solution
We can line up the numbers and subtract just as we do in base 10. For example, when we borrow from the s place, the digit 1 in the units place becomes , while the digit in the s place decreases by 1. Continuing in this way, we find \begin{array}{c@{}c@{}c@{}c@{}c}
& \cancelto{1}{2} & \cancelto{4}{1} & \cancelto{1}{2} & \cancelto{4}{1}_3 \\
-& & 2 & 1 & 2_3 \\
\cline{2-5}
& 1 & 2 & 0 & 2_3 \\
\end{array}So the difference is .
Final answer
1202_3