2008 Mock ARML 1 Problems/Problem 7
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 |