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smc

number theory intermediate

Problem

In the numeration system with base , counting is as follows: . The number whose description in the decimal system is , when described in the base system, is a number with:
(A)
(B)
(C)
(D)
Solution
Since , divide by . The quotient is and the remainder is , so rewrite the number as Similarly, dividing by results in quotient of and remainder of , so rewrite the number as Thus, the number in base can be written as , so the answer is
Final answer
C