how to write a function to find a unique triangle?

Lenght of triangle is L,which is an integer ,also the 3 sides are integer.

for Pythagorean theorem , for example,

L=12 can be composed by 3,4,5 or

L=30 from 5,12,13...

but when L=120,sides can be 30,40,50 or 20,48,52, this kind of triangle might not be considered.It can output(0,0,0).

How to write a function, which has as input a length L, and outputs triple(a,b,c) being the only triangle,where the sides( a b c ) all have integer L :otherwise it outputs(0,0,0).

Thanks a lot.

Answer 1

[John D'Errico]

Gosh. Do they give the identically same homework assignment to every kid in the entire world?

unique(sort(pythagSum(1234567890),2),'rows')
ans =
    63080361   584045440   587442089
    63627480   583741485   587198925
   123456789   548696840   562414261
   149857215   532003644   552707031
   180721521   511427440   542418929
   205761315   493827156   534979419
   258784215   453576204   522207471

I'll bet if you bother to look on this site, you will find the code that produced that result, and the idea on which it was based. Of course, if you submit my solution to this problem to your teacher, I'll expect a citation of my work.