Thread: Diophantine equations and Euler

Hi
I'm trying to find Euler's method for solving Diophanitne equations... at this stage only first order equations
Thanks in advance for the assistance

Originally Posted by delpin

Hi
I'm trying to find Euler's method for solving Diophanitne equations... at this stage only first order equations
Thanks in advance for the assistance

WHAT?!?

There is no specific way to solve a Diophantine equation. In fact some Diophantine equations cannot even be proven to they have no solutions! This was one of Hilbert's 23 Problems. Euler was able to prove them/solve them because he was talented.

You might be asking about Differencial equations but just confused the words with Diophantine equations. There is such a thing called Euler's method in the theory of differencial equations, maybe you are asking that?

I have found some information about Euclid and Diophantine Equations but I have been asked about Euler... and most definitely not differential equations

Originally Posted by delpin

I have found some information about Euclid and Diophantine Equations but I have been asked about Euler... and most definitely not differential equations

I can give a lecture on Diophantine equations (love them) if you want consisting in 3 parts:
1)Linear in two variables.
2)Pell's equation and countinued fractions.
3)Infinite Descent and Fermat's Last Theorem.

http://www.alpertron.com.ar/QUAD.HTM
does it find all solution? (integer of course)
tnx