### Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

### System Speak

Five equations... five unknowns... can you solve the system?

### Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

##### Age 16 to 18 Challenge Level:

There are six possible solutions to each of the following equations. Can you find them all?

1. $(n^2 - 5n + 5)^{(n^2 - 11n + 30)} = 1$

2. $(n^2 - 7n + 11)^{(n^2 - 13n + 42)} = 1$

Can you find some more Mega Quadratic Equations like these?

With thanks to Don Steward, whose ideas formed the basis of this problem.