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.
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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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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