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Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

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Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

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Age 16 to 18 Challenge Level:

If the integer part of $x$ is $a$ then $x=a + b$ where $a$ is a whole number and $0\leq b < 1$.

Try some numerical values of $x$, evaluate the three functions and record the results. What do you notice? Can you prove that different values of $x$ will produce similar findings?