Euclidean Algorithm/Examples/341 and 527/Integer Combination

Examples of Use of Euclidean Algorithm
$31$ can be expressed as an integer combination of $341$ and $527$:


 * $31 = 2 \times 527 - 3 \times 341$

Note also that:
 * $31 = 14 \times 341 = 9 \times 527$

and:
 * $31 = 13 \times 527 - 20 \times 341$

Proof
From Euclidean Algorithm: $341$ and $527$ we have:
 * $\gcd \set {341, 527} = 31$

Then we have: