2021 CIME I Problems/Problem 2
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Problem 2
For digits with
the positive integer
can be written as
in base
and
in base
. Find the base-
representation of
.
Solution
Consider the different representations of the number and equate them:
Note that c can't contribute since it is less than 5 so
Next note that
since
and
the only solution is
,
Thus in base 10 the number is