Discussion in 'New & Returning Members' started by 2g00d4u, Dec 13, 2000.
I got it (well, the theory at least).
Stop tryin to be all so 31337... The next t'ing you will say Magic playerz breed hackers (hax0rs)
and ohh... welcome...
Probably it would help if you spelled the word "Diophantine" - the
equations are named after Diophantus of Alexandria, a famous Greek
mathematician of antiquity.
A Diophantine equation is one equation in at least two variables, say
x and y, whose solutions (x,y) are required to be whole numbers
(integers). Some such equations have no solutions. Some have a finite
number. Some have infinitely many. The example of the Pythagorean
equation is one:
a^2 + b^2 = c^2.
If you are asked for integer solutions, this is a Diophantine
equation. You already know some solutions, I am sure:
(a,b,c) = (0,0,0), (0,1,1) (0,1,-1), (0,-1,1), (0,-1,-1), (1,0,1),
(1,0,-1), (-1,0,1), (-1,0,-1),
for example. You can see that for this equation, you can assume that
a, b, and c are all positive. From that solution you can obtain others
by changing signs of some or all of a, b, and c. Furthermore, you can
assume a <= b, since you can take any solution and swap a and b to get
another. In this case there are infinitely many solutions.
Another Diophantine equation might be 5*x + 7*y = 57. This, too, has
an infinite number of solutions, and they are given by x = 3 + 7*t,
y = 6 - 5*t, where t is any integer.
Hehe, neva' mind
That's some freaky mumbojumbo
Separate names with a comma.