Difference between revisions of "1987 OIM Problems/Problem 3"
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== 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. | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 12:49, 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.
Solution
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