Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 20, 2011"
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| − | {{ | + | Since it is both a perfect cube and a perfect square, it must be a perfect sixth power. This is because the GCD of <math>2</math> and <math>3</math> is <math>6</math>, meaning it will leave an integer power when either the square root or the cube root is taken. The fourth perfect sixth power is <math>4^6=2^{12}=\boxed{4096}</math>. |
Latest revision as of 22:10, 19 June 2011
Problem
AoPSWiki:Problem of the Day/June 20, 2011
Solution
Since it is both a perfect cube and a perfect square, it must be a perfect sixth power. This is because the GCD of 
and 
is 
, meaning it will leave an integer power when either the square root or the cube root is taken. The fourth perfect sixth power is 
.
