Difference between revisions of "2008 Mock ARML 1 Problems/Problem 7"
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== See also == | == See also == | ||
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[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] |
Latest revision as of 18:34, 29 May 2008
Problem
Compute the number of -digit base-
positive integer multiples of
that are also divisible by
when read in base
instead of base
.
Solution
Let the number be . Then
, and so it must divide their difference, so
, from which it follows that
. However, as
, we have
, leading to
solutions:
.
See also
2008 Mock ARML 1 (Problems, Source) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 |