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What is the smallest positive integer n such that \sqrt[4]{1323*n*84*779*5*3*441} is an integer?

 Oct 17, 2024
 #1
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Technically, the answer is 0 since sqrt[4](0) = 0, but if that's not it, then the second smallest integer is:

 

\(\sqrt[4]{1323*n*84*779*5*3*441}\)

 

\(1323 = 3^3 7^2\)

\(84 = 2^23^17^1\)

\(779 = 19^141^1\)

\(441 = 3^27^2\)

 

\(\sqrt[4]{1323*n*84*779*5*3*441} = 2^23^85^17^519^141^1\)

 

To make all exponents a multiple of four, n must be \(2^25^37^319^341^3 = \mathbf{81073047338500}\)

 Oct 17, 2024
 #2
avatar+135 
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edit: The answer can't be 0 since it must be a positive integer. The second bolded number is the correct answer

Maxematics  Oct 17, 2024

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