Mock AIME 3 Pre 2005 Problems/Problem 12
Determine the number of integers such that and is divisible by .
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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.