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jmc

number theory intermediate

Problem

Find the value of such that the following equation in base is true: \begin{array}{c@{}c@{}c@{}c@{}c@{}c} &&6&4&5&3_h\\ &+&7&5&1&2_h\\ \cline{2-6} &1&6&1&6&5_h.\\ \end{array}
Solution
The two rightmost columns do not result in any carrying; however, in the third column there is a residue of . Subtracting from the sum of and , we see that is .
Final answer
8