Does anyone know a general procedure to determine whether a diophantine equation - a polynomial equation with integer coefficients in several variables - has any solutions in integers?
OT: More Rule of Tim / Theory of Tim
Feb 14, 2004
9 Replies
I gather it can be done for first order diophantines, but a general solution has been proven impossible.
Try
formatting link
. This seems tosolve the problem of finding the integer coefficients, if that's what youwere after, but it doesn't give a general answer as to whether there areany, without actually working them out. HTH David
Well having failed to hunt out the relevant text upstairs you should at least ask something you can't google an answer to in seconds :-)
Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution. Such an algorithm does exist for the solution of first-order Diophantine equations. However, the impossibility of obtaining a general solution was proven by Yuri Matiyasevich in 1970
formatting link
Unless of course you are talking about another particular case.
If you are asking the question you should at least mention Fermat.
Alistair
Well yes, I have a proof, but its too long to fit in the margins of this email....
Or, as Fermat put it, now work it out yerselves,yer bastards.
Steve
If I were to say it has, then it has, they are only words after all.
Did Fermat really say that?
He was pissed at the time - and in the process of being thrown out of a brothel...
Martyn, sounds to me like you've only gone and opened that special bottle and consumed the majority of it........ Badger.
Go on, what the hell do you want to solve Diophantine equations for ?
Steve
in article c0nbop$18dc08$ snipped-for-privacy@ID-129032.news.uni-berlin.de, Larry at snipped-for-privacy@larry-arnold.com wrote on 15/2/04 8:46 am:
Does this apply if you don't understand them? ;-)
Join the Discussion
Have something to add? Share your thoughts — no account required.
Didn't find your answer?
Ask the community — no account required