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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 166

If
$$
P(X)=a_d\prod_{i=1}^d(X-\alpha_i),
$$
its <Mahler measure> is
$$
M(P)=|a_d|\prod_{i=1}^d\max(1,|\alpha_i|).
$$
If $f_\alpha\in\mathbb Z[X]$ is the primitive minimal polynomial of an algebraic number $\alpha$ and $d=\deg f_\alpha$, the <height-Mahler measure formula> is
$$
H(\alpha)^d=M(f_\alpha).
$$

Solved by gpt-5.6-sol high.

Solution

Paper 166 / 2 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 166 / 2 / a / Solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 166 / 2 / a / Solution

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