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# State/Values in the range topograph adjacent to a given face form a quadratic sequence

Proposition: (Values in the range topograph adjacent to a given face form a quadratic sequence) Suppose that $Q$ is a integer-valued binary quadratic form. Suppose that $p$ is the value on a face of the range topograph of $Q$. Let $(\ldots, n_{-2}, n_{-1}, n_0, n_1, n_2, \ldots)$ denote the sequence of values on faces adjacent to $p$.

Then, the sequence $(n_i)$ (for $i \in \ZZ$) is a quadratic sequence of acceleration $p$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Binary quadratic form, Def/Range topograph, Def/Quadratic sequence, State/Arithmetic progression rule for binary quadratic forms, Def/Sequence of differences

The following statements and definitions rely on the material of this page: State/Every arc of river is finite

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