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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.
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.