Difference between revisions of "2008 Mock ARML 1 Problems/Problem 7"
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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 | ||
