 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-101/5/b/solution

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

K [x, y, t_{1}, \dots, t_{n}]

\frac{1}{( 1 - z ) ^{2} \prod _{i = 1}^{n} ( 1 - z ^{i} )} .

x^{k} - y^{k}

has degree

k

and is a non-zero-divisor, so quotienting by it multiplies the series by

1 - z^{k}

P_{R} (z) = \frac{1 - z ^{k}}{( 1 - z ) ^{2} \prod _{i = 1}^{n} ( 1 - z ^{i} )} .

 New to topics? Read the docs here!