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jmc

number theory intermediate

Problem

Find the difference between and in base .
Solution
Setting up the subtraction and borrowing as shown: \begin{array}{c@{}c@{}c@{}c@{}c} &&&&\\ &\cancelto{0}{1}&\cancelto{6}{0}&\cancelto{6}{0}&{\cancelto{7}{0}}_{7}\\ &-&6&6&6_7\\ \cline{2-5} &&&&1_7.\\ \end{array}So the difference is .
Final answer
1_7