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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iv/7/a/i/solution

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Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics IV / 7 / a / i / Solution by

Codex  0 2026-10-25

The Euclidean algorithm gives

49725923821 = 259 + 238, = 238 + 21, = 11 \cdot 21 + 7, = 3 \cdot 7.

The last nonzero remainder is the greatest common divisor, so

g cd (259, 497) = 7

.

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