A method for finding solutions 
and 
to a linear congruence
 |
by constructing a matrix formed by adjoining a vector containing 
and 
with a unit matrix,
![M=[a 1 0; b 0 1],](/images/equations/BlankinshipAlgorithm/NumberedEquation2.svg) |
and applying the Euclidean algorithm to the first column, while extending the operations to all rows. The algorithm terminates
when the first column contains the greatest
common divisor 
.
