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Exhaustion
Age 16 to 18
Challenge Level 
Perhaps you might like to try the problem Unit Fractions first.
What value does the expression take for small values of a?
What value does the expression take for large values of a?
When you try a particular value for a what can you say about b?
Once you have narrowed down the possible values, you have to test all possible cases; this is known as proof by exhaustion.
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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?
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.
