## Friday, June 28, 2013

### Plots of x^t + y^t = n^t (x, y, n are integers)

Happy Friday almost July 2013!

This is a series of plots of the following:

1. x^2 + y^2 = n^2
2. x^2 + y^2 = n^3
3. x^3 + y^3 = n^2
4. x^3 + y^2 = n^2
5. x^3 + y^2 = n^3

For x, y, and n all integers. Plots are pointed for combinations where the result, n, is an integer. The range tested is 0 ≤ x ≤ 200 and 0 ≤ y ≤ 200. I used the TI nSpire CX CAS iOS app.

How many points?

1. x^2 + y^2 = n^2, 703 points
2. x^2 + y^2 = n^3, 55 points
3. x^3 + y^3 = n^2, 97 points
4. x^3 + y^2 = n^2, 375 points
5. x^3 + y^2 = n^3, 213 points, mostly when y=0

Program Outline: (for plot 1, similar format for the rest)
Define test()
Prgm
xs:={ }
ys:={ }
For k,0,200
For l,0,200
If iPart(√(k^2+l^2))=0 Then
xs:=augment(xs,{k})
ys:=augment(ys,{l})
EndIf
EndFor
EndFor
EndPrgm

And now to the fun part... Enjoy!

That's it for now - as always thanks for your support and words of encouragement and your questions. :)

Eddie

This blog is property of Edward Shore. 2013