Can the equations x and y be found using the vector

Does this work?

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- Jun 25th 2010, 01:26 PMdwsmithLinear Diophantine Equations

Can the equations x and y be found using the vector

Does this work? - Jun 25th 2010, 03:05 PMjamix
I'm not sure I understand your two vectors and .

It is true that is a solution to the equation and that the general solution is of the form where are integer constants, however in this case the constants are not but rather .

Can you see why?

Hence the general solution is and - Jun 25th 2010, 03:20 PMdwsmith
There aren't two vectors. That is why I said vector not vectors. The vector is denoted and denotes a point.

You know how if you have a vector and a point you can parametrize it? Can that be done for these types of equations? - Jun 25th 2010, 04:16 PMjamix
It depends on whether or not the point is a solution the equation.

Regardless of the point used as your initial solution , there is only ONE vector that can be used to describe the entire set of solutions as

Is this what you wanted? - Jun 25th 2010, 07:49 PMchiph588@