 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-1/1g/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

a x + b y = c

has an integer solution exactly when

g cd (a, b)

divides

c

231410073001078621 = 2 (1007) + 300, = 3 (300) + 107, = 2 (107) + 86, = 86 + 21, = 4 (21) + 2, = 10 (2) + 1.

Thus

g cd (1007, 2314) = 1

, which divides

37

. Therefore

1007 x + 2314 y = 37 has integer solutions .

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