# Linear diophantine equation in n variables

Let n>3. Is there any way to generate all integer solutions of linear diophantine equation in n variables, or at least to determine number of such solutions?

Say if $\sum_{i=1}^k a_ix_i = N$ is the equation with $gcd(a_i,a_j)=1$ if $i\neq j$, then if we seek solutions $x_i:0\leq x_i<a_i$, then is the solution unique? – Turbo Sep 14 '13 at 17:15