Euclidean Algorithm/Examples/12378 and 3054/Integer Combination

Examples of Use of Euclidean Algorithm
$6$ can be expressed as an integer combination of $12378$ and $3054$:


 * $6 = 132 \times 12378 - 535 \times 3054$

Note also that:
 * $6 = 3186 \times 12378 - 12913 \times 3054$

by adding $3054 \times 12378$ to both sides.

Proof
From Euclidean Algorithm: $12378$ and $3054$ we have:
 * $\gcd \set {12378, 3054} = 6$

Then we have: