### Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

### 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.

### After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

# Shades of Fermat's Last Theorem

##### Stage: 5 Challenge Level:

Investigate what happens when you put $n=2$ in the expression. Then try $n=3$, $4$ and $5$.