Integer solutions for multiple variable equations

[MagnusM]

Obviously it will take some brute-force. But how do I minimize the brute-force needed (optimize)? I know one can solve Diophantine equations and quadratic Diophantine equations. But what if I have something like 10 (any number) of variables?

(what if there are no squares, what if there are cubes, other powers fck it gimme everything i can read, bring it on :D)

I don't want you to give me a step by step solution. Could you just push me in the right direction? What are the techniques used for solving this called for example or what are good reads on the subject related to this?

(Does a general solution exist? Will the solutions make up a set/series which can be described as a pattern?) I know I can bruteforce specific solutions, but can I write the solution as a series and what would be the best way of finding it?

If you want me to be specific 7391049=a^2 + 8b^2 + 27c^2 + 64d^2 + 125e^2 + 216f^2 + 343g^2 + 512h^2 + 729i^2 + 1000j^2 + 1331k^2

 

[jedishrfu]

I think you'll need a computer to try all combos but even then it may never find an integer solution.

Here's an example of solving a simpler diophantine equation by inspection with a book reference for other tricks:

http://mathforum.org/library/drmath/view/51543.html

ALSO, Please refrain from posting obscenities even as 3 letter words or through other leet speak tricks:

http://en.wikipedia.org/wiki/Leet_speak

otherwise someone will either report it or your thread will disappear mysteriously...

ALSO, please edit your post NOW to remove it.

Thanks PF will appreciate it.