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The hints are written into the question. If you can do a little simple algebra, solve quadratic equations and argue through a proof by induction, then you can sail through this question.
Golden Fractions
Age 16 to 18
Challenge Level 
The hints are written into the question. If you can do a little simple algebra, solve quadratic equations and argue through a proof by induction, then you can sail through this question.
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Good Approximations
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
There's a Limit
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Not Continued Fractions
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?