Finding the Maximum Value of n for a Given Equation

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SUMMARY

The discussion centers on finding the maximum value of n for the equation where a multiple of 4 is less than n² but greater than n² + 2016/n². The equation n² < n² + 2016/n² is established as a foundational inequality. Participants conclude that the paradox arises from the impossibility of a number being simultaneously less than and greater than the defined bounds, indicating that no valid n exists under these conditions.

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Marcelo Arevalo
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What is the Largest possible value of n such that there is a multiple of 4 less than n^2 but greater than n^2 + 2016/n^2 ?
 
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I think you will agree that:

$$n^2<n^2+\frac{2016}{n^2}$$

So, how can some number be smaller than the smaller value, and at the same time greater than the greater value?
 
Meaning, there's no such thing as the smaller value, and at the same time greater than the greater value?
 

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