1988 OIM Problems/Problem 2

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Problem

Let $a$, $b$, $c$, $d$, $p$, and $q$, be non-zero natural numbers that verify $ad-bc=1$, and $\frac{a}{b} >\frac{p}{q}>\frac{c}{d}.

Prove:

(i)$ (Error compiling LaTeX. Unknown error_msg)q \ge b+d$(ii) If$q=b+d$, then$p=a+c$.

Solution

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