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jmc

number theory intermediate

Problem

Express

4321 0_{6} - 321 0_{7}

in base 10.

Solution

We convert to base 10 to obtain

4321 0_{6} = 4 \cdot 6^{4} + 3 \cdot 6^{3} + 2 \cdot 6^{2} + 1 \cdot 6^{1} + 0 \cdot 6^{0} = 5910.

321 0_{7} = 3 \cdot 7^{3} + 2 \cdot 7^{2} + 1 \cdot 7^{1} + 0 \cdot 7^{0} = 1134.

Therefore,

5910 - 1134 = 4776

.

Final answer

4776