What are diophantine equations? And what is Fermat's method of infinite descent? Can anyone provide me some good resources on the web for learning them in detail?

EDIT. Can someone on MHF start a tutorial on Number theory? It would be very nice.

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- Aug 6th 2008, 06:02 AMfardeen_genWhat are diophantine equations?
What are diophantine equations? And what is Fermat's method of infinite descent? Can anyone provide me some good resources on the web for learning them in detail?

EDIT. Can someone on MHF start a tutorial on Number theory? It would be very nice. - Aug 6th 2008, 10:16 AMThePerfectHacker
It is an equation where the solution is in terms of positive integers.

For example, solve $\displaystyle x^3+y^3=z^3$.

It turns out this equation has no solution - proving that is a lot more complicated.

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And what is Fermat's method of infinite descent?

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EDIT. Can someone on MHF start a tutorial on Number theory? It would be very nice.

- Aug 6th 2008, 02:39 PMMoo
Hello,

Basically, it's an equation of this form : P(x,y,z)=0.

P is a polynomial with x,y,z as variables and such that the coefficients are integers or rational numbers.

The solutions are also searched in the range of integers or rational numbers.

Talkin' about Fermat, the example TPH provided is an element of Fermat's last theorem : $\displaystyle x^n+y^n=z^n$ has no integer solution for $\displaystyle n>2$ (Tongueout)