Linear diophantine equation.

1. Mar 25, 2008

mhill

1. The problem statement, all variables and given/known data

given any linear diophantine equation in n-variables, is there a method to solve it

2. Relevant equations

the general diophantine equation is $$a_{0}x_0 + a_{1} x_{1} + a_{2} x_{2} +......+a_{j} x_{j} = N$$ j=1,2,3,...

and i suppose we should impose that the g.c.d of all the a(n) integers is 1 so the equation has a solution

3. The attempt at a solution

for the case j=1 and ax+by=c i know how to solve it but i would need a hand for the higher dimensional case , perhaps with an example in 4 o 5 variables solved i could obtain a general method thanks.

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