For coprime integers $p,q$ with $q>0$,
$$
H(p/q)=\max\{|p|,q\}.
$$
This follows either directly from the real and <p-adic absolute value>[p-adic absolute values], or from the <height-Mahler measure formula> applied to the primitive <minimal polynomial> $qX-p$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 166 / 2 / f / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-166/2/f/solution