View source for 1988 OIM Problems/Problem 2

== 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</math>, and <math>\frac{a}{b} >\frac{p}{q}>\frac{c}{d}</math>.

Prove:

(i) <math>q \ge b+d</math>

(ii) If <math>q=b+d</math>, then <math>p=a+c</math>.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

== Solution ==
{{solution}}

== See also ==
https://www.oma.org.ar/enunciados/ibe3.htm