Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 13"
m (Created page with "== Problem == == Solution == == See also == {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=12|num-a=14}} Category:Intermediate Number Theory Problems") |
m (→Problem) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | Let <math>S</math> be the set of positive integers with only odd digits satisfying the following condition: any <math>x \in S</math> with <math>n</math> digits must be divisible by <math>5^n</math>. Let <math>A</math> be the sum of the <math>20</math> smallest elements of <math>S</math>. Find the remainder upon dividing <math>A</math> by <math>1000</math>. | ||
| + | |||
| + | == Solution == | ||
== Solution == | == Solution == | ||
Latest revision as of 20:20, 8 October 2014
Contents
Problem
Let 
be the set of positive integers with only odd digits satisfying the following condition: any 
with 
digits must be divisible by 
. Let 
be the sum of the 
smallest elements of . Find the remainder upon dividing by 
.
Solution
Solution
See also
| Mock AIME 5 2005-2006 (Problems, Source) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
