If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of
these numbers must be 1. Now for the complexity! When are the other
numbers real and when are they complex?

The sum of any two of the numbers 2, 34 and 47 is a perfect square.
Choose three square numbers and find sets of three integers with
this property. Generalise to four integers.

System Speak

Stage: 5 Challenge Level:

Take a look at the system of equations below:

$ab = 1$

$bc = 2$

$cd = 3$

$de = 4$

$ea = 6$

Can you find a set of values {a, b, c, d, e} that satisfy the system?
Can you find more than one?