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2007 AMC 10B Problem 25

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2007 AMC 10B Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Diophantine Equations · difficulty 5 of 5 · about 8 min · position P21-25

How many pairs of positive integers (a,b)(a,b) are there such that aa and bb have no common factors greater than 11 and:

ab+14b9a\frac{a}{b} + \frac{14b}{9a}

is an integer?

  1. A)

    44

  2. B)

    66

  3. C)

    99

  4. D)

    1212

  5. E)

    infinitely many\text{infinitely many}

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