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## Saturday, August 20, 2011

### Exercise

Exercise:
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 $q$.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)