![Making Waves](/sites/default/files/styles/medium/public/thumbnails/content-01-01-15plus5-icon.jpg?itok=-u6n_Zqq)
Inequalities
![Making Waves](/sites/default/files/styles/medium/public/thumbnails/content-01-01-15plus5-icon.jpg?itok=-u6n_Zqq)
![Rationals Between...](/sites/default/files/styles/medium/public/thumbnails/content-01-01-15plus1-icon.jpg?itok=mgB7j3uT)
![Code to Zero](/sites/default/files/styles/medium/public/thumbnails/content-00-12-15plus2-icon.jpg?itok=tHiJqly5)
problem
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.
![Exhaustion](/sites/default/files/styles/medium/public/thumbnails/content-00-09-15plus4-icon.jpg?itok=J-ZMZTPI)
![Two Cubes](/sites/default/files/styles/medium/public/thumbnails/content-99-09-15plus1-icon.png?itok=YT23adOn)
problem
Two Cubes
Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]
![Shades of Fermat's Last Theorem](/sites/default/files/styles/medium/public/thumbnails/content-99-03-15plus2-icon.jpg?itok=8CIbS9e1)
problem
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?
![Proofs with Pictures](/sites/default/files/styles/medium/public/thumbnails/content-00-11-art1-icon.gif?itok=Yalq6fVl)