 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-3/1g/a/solution

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

Write

f = [a, b, c]

f

and

g

are equivalent if there is a matrix

U = (α γ β δ) \in SL_{2} (Z)

such that

g (x, y) = f (αx + β y, γ x + δy) .

Equivalently, the group

SL_{2} (Z)

acts on forms by integral unimodular changes of variables.

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