Find two Pythagorean triples with sides A,B,C and D,E,F such that all these relationships are simultaneously satisfied:
(i) A+D is a cube
(ii) B+E is a cube, and:
(iii) C+F is a cube.
[Edit: the title of the comment is supposed to read:
"Solution if A<B<C and D<E<F not required"
Apparently the symbols < and > cannot be in a comment title.]
It is not stipulated that A,B,C and D,E,F are necessarily in increasing order.
If they are not so constrained, then a solution is:
two triples:
(125, 300, 325) and (875, 15325, 15300)
produce sums of :
(1000, 15625, 15625)
which are cubes of :
(10, 25, 25)
If the listing of A,B,C in a Pythagorean triple is inherently defined as being in increasing order, then this does not constitute a valid solution.
----------------
The program is nearly the same as for Pythagorean Triples #1 except for a few lines.
Edited on February 9, 2024, 11:28 am
|
|
Posted by Larry
on 2024-02-09 11:26:45 |
Solution if A