Difference between revisions of "1987 OIM Problems/Problem 3"
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<cmath>1+m+n\sqrt{3}=[2+\sqrt{3}]^{2r-1}</cmath> | <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 13:27, 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
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