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1988 OIM Problems/Problem 2

Revision as of 12:01, 13 December 2023 by Tomasdiaz (talk | contribs) (→‎Problem)

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) $q \ge b+d$

(ii) If $q=b+d$, then $p=a+c$.

Solution

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