Difference between revisions of "1989 AIME Problems/Problem 9"

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== Problem ==
 
== Problem ==
Let <math>a_{}^{}</math>, <math>b_{}^{}</math>, <math>c_{}^{}</math> be the three sides of a triangle, and let <math>\alpha_{}^{}</math>, <math>\beta_{}^{}</math>, <math>\gamma_{}^{}</math>, be the angles opposite them. If <math>a^2+b^2=1989^{}_{}c^2</math>, find
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One of Euler's conjectures was disproved in then 1960s by three American mathematicians when they showed there was a positive integer such that <math>133^5+110^5+84^5+27^5=n^{5}_{}</math>. Find the value of <math>n^{}_{}</math>.
<center><math>\frac{\cot \gamma}{\cot \alpha+\cot \beta}</math></center>
 
  
 
== Solution ==
 
== Solution ==

Revision as of 22:14, 24 February 2007

Problem

One of Euler's conjectures was disproved in then 1960s by three American mathematicians when they showed there was a positive integer such that $133^5+110^5+84^5+27^5=n^{5}_{}$. Find the value of $n^{}_{}$.

Solution

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See also

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