1-12-10: Fermat's Last Theorem

Wired.com had a nice little piece in honor of Pierre de Fermat, who died on this date in 1665. Fermat is probably most well known for his Last Theorem, which pretty much states that:
No integer combination exists such that x^n + y^n = z^n for n greater than 2.

It took centuries to prove the theorem.

In honor of Fermat, I put together a quick MATLAB script to find the combinations for x^2 + y^2 = z^2, for integers between 1 and 100. Here it is:

clear
clc
n = 100;
disp('Start!')
for i = 1:n
for j = 1:n
for k = 1:n
if i^2 + j^2 == k^2
disp([i,j,k])
end
end
end

end
disp('End!')


Here are the results (with duplicate x’s and y’s removed; e.g. 3^2 + 4^2 = 5^2 == 4^2 + 3^2 = 5^2):

3 4 5
5 12 13
6 8 10
7 24 25
8 15 17
9 12 15
9 40 41
10 24 26
11 60 61
12 16 20
12 35 37
13 84 85
14 48 50
15 20 25
15 36 39
16 30 34
16 63 65
18 24 30
18 80 82
20 21 29
20 48 52
21 20 29
21 28 35
21 72 75
24 32 40
24 45 51
24 70 74
25 60 65
27 36 45
28 45 53
28 96 100
30 40 50
30 72 78
32 60 68
33 44 55
33 56 65
35 84 91
36 48 60
36 77 85
39 52 65
39 80 89
40 42 58
40 75 85
42 56 70
45 60 75
48 55 73
48 64 80
51 68 85
54 72 90
57 76 95
60 63 87
60 80 100
65 72 97

Couldn’t get anything to work for x^3 + y^3 = z^3, of course.