 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/9e/iii/solution

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

b^{k} = 0

, then

(u + b)^{- 1} = u^{- 1} \sum_{j = 0}^{k - 1} (- b u^{- 1})^{j}

. For the polynomial, its positive-degree part is nilpotent by (ii), so adding it to the unit

a_{0}

gives a unit.

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