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Shades of Fermat's Last Theorem
Age 16 to 18
Challenge Level 
There are exactly three solutions of the equation $$(x - 1)^n + x^n = (x + 1)^n$$ where $x$ is an integer and $n= 2, 3, 4$ or $5$. Prove this statement and find the solutions.
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Code to Zero
Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.
