### 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?

### 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.

# In Between

##### Stage: 5 Challenge Level:
Well done to Minhaj, Amrit, Adithya, Sasi, Will, Charlie, Luke and Luke, Eric, Pablo, Julian, Johnny, Peter, Gabriel, and Manolis for their hard work on this problem!

$$x^2-14x+1< 0.$$
Use the quadratic formula to solve this inequality. From the graph of $y =x^2 -14x + 1$ we see that the solution is $7-4\sqrt 3 < x < 7+4\sqrt 3$ or approximately $0.072< x< 13.928.$