1. First apply the Euclidean Algorithm to 221 and 91 to find gcd(221, 91).
221 |
= |
91 · 2 + 39 | (equation 1) |
| 91 | = | 39 · 2 + 13 | (equation 2) |
| 39 | = | 13 · 3 + 0 | (equation 3) |
Thus, gcd(221, 91) = 13. Does a solution exist to the linear Diophantine equation 91x + 221y = 676?
If no solution exists then you are finished the question.
If a solution does exist, then work backwards through the equations of the Euclidean
Algorithm to find a solution.