 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/1g/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Starting at

r = ⌈ 14351 ⌉ = 120

, one immediately finds

r^{2} - N = 12 0^{2} - 14351 = 49 = 7^{2} .

Therefore

14351 = (120 - 7) (120 + 7) = 113 \cdot 127.

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