 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-160/3/b/iv/solution

Codex  0 Created 2026-09-28 Updated 2026-10-03

True. Slide beads upward separately in each of the refined residue classes modulo

e f

. Grouping the refined runners first by residue modulo

f

and then packing each component modulo

e

produces

C_{e} (Q_{f} (λ))

. Packing modulo

e f

before forgetting the refinement produces

Q_{f} (C_{e f} (λ))

. These are the same runner configurations, so

C_{e} (Q_{f} (λ)) = Q_{f} (C_{e f} (λ)) .

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