2. First apply the Euclidean Algorithm to 105 and 56 to find gcd(105, 56).
105 |
= |
56 · 1 + 49 |
| 56 | = | 49 · 1 + 7 |
| 49 | = | 7 · 7 + 0 |
Thus, gcd(105, 56) = 7. Does a solution exist to the linear Diophantine equation 105m + 56n = -14?
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.