Difference between revisions of "1987 OIM Problems/Problem 3"
(Created page with "== Problem == Prove that if <math>m</math>, <math>n</math>, and <math>r</math> are non-zero positive integers, and <cmath>1+m+n\sqrt{3}=\[2+\sqrt{3}]^{2r-1}</cmath> then <math...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
Prove that if <math>m</math>, <math>n</math>, and <math>r</math> are non-zero positive integers, and | Prove that if <math>m</math>, <math>n</math>, and <math>r</math> are non-zero positive integers, and | ||
| − | <cmath>1+m+n\sqrt{3}= | + | <cmath>1+m+n\sqrt{3}=[2+\sqrt{3}]^{2r-1}</cmath> |
then <math>m</math> is a perfect square. | then <math>m</math> is a perfect square. | ||
| + | |||
| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe2.htm | ||
Latest revision as of 12:27, 13 December 2023
Problem
Prove that if 
, 
, and 
are non-zero positive integers, and
![\[1+m+n\sqrt{3}=[2+\sqrt{3}]^{2r-1}\]](http://latex.artofproblemsolving.com/9/1/5/915befa846798acdafe765d0ea82c08321e86dea.png)
then is a perfect square.
~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.
