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2007 AMC 10B Problems/Problem 25

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How many pairs of positive integers (a,b) are there such that a and b have no common factors greater than 1 and:

\mathrm frac {a}/{b} + \mathrm frac {14b}/{9a}

is an integer?

(A) 4

(B) 6

(C) 9

(D) 12

(E) infinitely many

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