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Saturday, August 20, 2011


Find $x, y$ such that $$\frac{1}{x} + \frac{1}{y} = \frac{1}{pq}$$ where $x,y \in \mathbf{Z}$ and $p,q$ are prime.

Hint: there are nine different solutions. I'll publish the method and solution on request ( comment ).


  1. Hmm, I see lots more than 9 solutions. I started with 1/3 + 1/6 = 1/2, and multiplied both sides by 1/p. I wonder if you meant something different...

  2. @Sue, $\frac{1}{x} + \frac{1}{y} = \frac{1}{15}$, has nine solutions, i.e. $(16, 240), (30,30)$, and another $7$ solutions. ;-)

  3. @Sue, so given $p,q$ you need to find nine pairs of solutions for $(x,y)$ and express them in terms of $p$ and $q$.


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