Diophantine Equation?

Question

Can someone explain to me what is a diophantine equation? thanks!!!

Answer 1

It's an equation that allows only integer solutions...
For instance the equation
2x + 4 = 0
has integer solution. It's x = -2
But the equation
2x + 1 = 0 has no integer solutions, although it has a real solution x = -1/2

Answer 2

A Diophantine equation is an equation in which only integer solutions are allowed.

Answer 3

Diophantos of Alexandria (c. 200 - 285 A.D.) was a highly accomplished mathematician of antiquity, one of whose books (Arithmetica) was rediscovered in late mediaeval times, to the complete astonishment of leading so-called mathematicians of the time who had struggled fruitlessly with many of the problems he had elegantly solved over a thousand years before them. It was in the margin of his copy of Diophantos' Arithmetica that Fermat regretfully wrote that it was too small to contain the proof of his famous Last Theorem.

Much of Diophantos' book is concerned with difficult equations for which solutions have to be found with INTEGER values of the unknowns. Linear Diophantine equations, with no squares or higher powers of the variables, are mere schoolboy problems and were quite beneath Diophantos' notice. Nevertheless, they are the only kind that most of us can manage, and they are called Diophantine equations even though he would have regarded them as trivial. Real Diophantine equations are HARD.

Answer 4

it is an equation like 3x + y = 0
but the solutions are the restclasses mod p
that is the rest of a nu,mber when divided by p.

for instance 3x + y = 0 mod 4 has as solutions
x=0,y=0, x=1,y=3, x=2,y=2,x=3,y=1

x=3,y=1 since 3*3 + 1 = 8 = 0 mod 4 ( 8/4 = 2 rest 0 )

o sorry , a diophantic equation is an equation where only integers are allowed as solution ( google )

Answer 5

Have a look at this link for an article I wrote on Diophantine Equations and how to solve them:

http://www.bbc.co.uk/dna/h2g2/A964956

Answer 6

To practice that 40 3 is minimum utilising a operating computer or computing gadget should be person-friendly, truly for someone who masters those children. For any (p,q,r) with 0<= p<= q

Answer 7

gjmb thinks that 3 * 3 + 1 = 8. What use is that?