Competition problem — Number theory

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Number theory Difficulty 6.1 National olympiad Prove it

1. Let $a / b$ be a rational fraction, $\left\langle a_{0}, \cdots, a_{n}\right\rangle$ be its finite simple continued fraction, $b \geqslant 1$ . Prove:
$a k_{n-1}-b h_{n-1}=(-1)^{n+1}(a, b)$

Solution

1. Derive from equations (4) and (5).

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