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jmc

number theory intermediate

Problem

Add Express your answer in base 3.
Solution
We may sum in base 3 just as in base 10. For example, in the rightmost column, the digits sum to 6. Since we are working in base 3, we record the remainder 0 as the rightmost digit in the sum and carry the quotient 2 to the next column. Continuing in this way, we find \begin{array}{c@{}c@{}c@{}c@{}c@{}c} & & 2 & 1 & 2 & 1_3 \\ & & & 2 & 1 & 2_3 \\ & & & & 1 & 2_3 \\ & + & & & & 1_3 \\ \cline{2-6} & 1 & 0 & 2 & 0 & 0_3, \\ \end{array}so the sum is .
Final answer
10200_3