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1988 OIM Problems/Problem 2

Revision as of 13:01, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>a</math>, <math>b</math>, <math>c</math>, <math>d</math>, <math>p</math>, and <math>q</math>, be non-zero natural numbers that verify <math>ad-bc=1</ma...")
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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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