MHB Finding the Maximum Value of n for a Given Equation

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The discussion revolves around finding the largest value of n for which a multiple of 4 exists between n^2 and n^2 + 2016/n^2. It is established that n^2 is less than n^2 + 2016/n^2, leading to confusion about the existence of a number that fits the criteria. Participants question the logical consistency of having a number that is both less than and greater than defined bounds. The core issue lies in reconciling the mathematical conditions set by the equation. Ultimately, the conversation highlights the complexities of the problem and the need for clarity in defining the parameters.
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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