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Shades of Fermat's Last Theorem

The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n + x^n = (x+1)^n so what about other solutions for x an integer and n= 2, 3, 4 or 5?

Upsetting Pitagoras

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

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Lattice Points

Age 16 to 18 Challenge Level:
The idea for this problem came from a Note in the Mathematical Gazette, Volume 20, July 2006 by Thomas Koshy entitled 'Lattice points in a family of hyperbolas'.

Even if you find some lattice points by trial and error you will still have to prove that there are no other possibilities.