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jmc

number theory intermediate

Problem

Find the sum of , and in base .
Solution
Setting up the terms in a descending order, the first column gives you a residue of and you carry over . In the second column there is no residue but you carry over . Finally, in the third column, the sum of gives you a residue of and you carry over . \begin{array}{c@{}c@{}c@{}c@{}c}&_{1}&_{2}&_{2}&\\&&5&5&5_6\\&&&5&5_6\\&+&&&5_6\\ \cline{2-5} &1&1&0&3_6\\ \end{array}Thus, the answer is .
Final answer
1103_6