- #1
e(ho0n3
- 1,357
- 0
Suppose I have a system of m equations in k unknowns
[tex]
\begin{align*}
a_{11}x_1 + a_{12}x_2 + \cdots + a_{1k}x_k &= 0 \pmod d \\
&\vdots \\
a_{m1}x_1 + a_{m2}x_2 + \cdots + a_{mk}x_k &= 0 \pmod d
\end{align*}
[/tex]
with the restriction that [itex]0 \le x_n < n[/itex]. How do I solve such a thing? Will Gaussian elimination work? What if I get a solution where one of the x's is outside its bounds?
[tex]
\begin{align*}
a_{11}x_1 + a_{12}x_2 + \cdots + a_{1k}x_k &= 0 \pmod d \\
&\vdots \\
a_{m1}x_1 + a_{m2}x_2 + \cdots + a_{mk}x_k &= 0 \pmod d
\end{align*}
[/tex]
with the restriction that [itex]0 \le x_n < n[/itex]. How do I solve such a thing? Will Gaussian elimination work? What if I get a solution where one of the x's is outside its bounds?