Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 12"
God of Math (talk | contribs) (→Solution) |
|||
| Line 4: | Line 4: | ||
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | We see a pattern when we look at the numbers that do fulfull this property. The first number is <math>1</math>. Then <math>3, 8, 9, 24, 27, ....</math>. This follows a pattern. The first number being <math>1</math>, and the rest being the previous <math>+2, +5, +1, +15, +3, +19, +3, +15, +1, +5, +2</math>. This sequence then repeats itself. We hence find that there are a total of <math>11*15 - 1</math> or <math>\boxed{164}</math> numbers that satisfy the inequality. | ||
==See also== | ==See also== | ||
Revision as of 17:18, 25 April 2009
Problem
Determine the number of integers 
such that 
and 
is divisible by 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
We see a pattern when we look at the numbers that do fulfull this property. The first number is 
. Then 
. This follows a pattern. The first number being , and the rest being the previous 
. This sequence then repeats itself. We hence find that there are a total of 
or 
numbers that satisfy the inequality.
