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

Revision as of 23:14, 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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 == 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
+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 ==

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

Revision as of 23:14, 24 February 2007

Problem

Solution

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