Re: a^2+b^2+c^2=45 when a+b+c=11
negative integers are not allowed.
I require all solutions.
If it could somehow be possible to get one solution and then from there calculate the rest of the solutions with respect to the first solution. But it seems that there is no way you can relate the first solution to any subsequent solutions.
When I initially approached this problem, i was expecting that there would be some sort of pattern that could be identified in the integers that would alllow us to then automatically get values for a different set of equations. But it seems there is no predictable pattern.
Kind of line with 1, 2, 3, 4, 5, 6 etc
This sequence is simple, you always know the next integer. Just add one from the last. but when you square things, the pattern disappears, or becomes a whole lot more complex.
Re: a^2+b^2+c^2=45 when a+b+c=11
Quote:
Originally Posted by Lucia333
I require all solutions
OK, I think this pretty much eliminates the optimization approach - that would only provide the solution closest to the initial guess, much like Newton Raphson for finding roots.
So, it seems we need ALL solutions for:
a + b + c + d .... = t
a2 + b2 + ..... = w
where
0 < a < b < c < d ..... are integers.
I've run out of ideas. I think the brute force all possible combinations approach is the only way, perhaps optimized to eliminate many out of bounds combinations. Maybe there is some sort of stastically based search that could help limit things, but that's beyond me.
Re: a^2+b^2+c^2=45 when a+b+c=11
i guess its beyond me too.
It looks like we should put this one to rest :(
not currently possible to do...
Re: a^2+b^2+c^2=45 when a+b+c=11
I think it can be done - it's just a question of how much computation time (seconds, minutes, hours) is needed depending on problem size. If this is a 'real time' application, then you'd probably want fractions of a second......just use massively parallel computers!:D
This problem looks like a good candidate for a PhD thesis.
