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BT.. Eat Your Heart Out
Age 16 to 18
Challenge Level 
The original number is $10000x + y$. What is the new number in terms of $x$ and $y$? Use the information to write down a Diophantine equation.
(The article on Euclid's Algorithm might help with this problem.)
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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?
