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.

Making Waves

Age 16 to 18
Challenge Level

Why do this problem?

This problem requires students to sketch graphs of trig functions, and think about the symmetries of these graphs. They are also required to think about inequalities and how they might show thee to be true.

For the last part of the problem there are a couple of suggested approaches in the Getting Started section.