Simple and not-so-tricky (really)

Algebra Level 3

Find the smallest natural number n n which satisfies the inequality 2016 1008 < n 2016 { 2016 }^{ 1008 }<{ n }^{ 2016 } .


The answer is 45.

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1 solution

Ponhvoan Srey
Mar 5, 2016

2016 1008 < n 2016 2016 1008 2016 < n 2016 2016 n > 2016 { 2016 }^{ 1008 }<{ n }^{ 2016 }\\ \sqrt [ 2016 ]{ { 2016 }^{ 1008 } } <\sqrt [ 2016 ]{ { n }^{ 2016 } } \\ \Rightarrow \quad n>\sqrt { 2016 } \\

The smallest natural number n n is therefore 45.

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