Difference between revisions of "1988 OIM Problems/Problem 2"
(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...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
== Problem == | == 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}. | + | 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: | Prove: | ||
| − | (i) < | + | (i) <math>q \ge b+d</math> |
| − | (ii) If < | + | (ii) If <math>q=b+d</math>, then <math>p=a+c</math>. |
| + | |||
| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe3.htm | ||
Latest revision as of 12:28, 13 December 2023
Problem
Let 
, 
, 
, 
, 
, and 
, be non-zero natural numbers that verify 
, and 
.
Prove:
(i) 
(ii) If 
, then 
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
