 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability-resit/3/b/solution

23921748644460184 = 1748 + 644, = 2 \cdot 644 + 460, = 460 + 184, = 2 \cdot 184 + 92, = 2 \cdot 92.

The last nonzero remainder is $g = 92$ . Back-substitution produces its Bézout coefficients:

92 = 460 - 2 \cdot 184 = 3 \cdot 460 - 2 \cdot 644 = 3 \cdot 1748 - 8 \cdot 644 = - 8 \cdot 2392 + 11 \cdot 1748.

Thus $(m, n) = (- 8, 11)$ is a requested pair. The final equality independently checks the calculation.

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