Finding Positive Integer Solutions for (2^n+1)/(n^2)

  • Thread starter Davewilliams
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In summary, The conversation discusses finding all positive integer answers for ((2^n)+1)/(n^2) where n is an integer greater than one. The speaker mentions using a program to brute force the answer, but is not sure how to solve it. They also reveal that the question originated from a friend at school and it is not a homework problem.
  • #1
Davewilliams
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Find all positive integer answers for ((2^n)+1)/(n^2) where n is an integer greater then one.
The only answer i can find is three, i wrote a program to brute force it and have gotten up to n=32000 but as for going about solving it i have no clue.
 
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  • #2
Where did this question orginate?
 
  • #3
A friend from school broght it in... I have no clue where he got it from though.
 
  • #4
Davewilliams said:
A friend from school broght it in... I have no clue where he got it from though.

Is it homework?
 
  • #5
No, its just a problem we where trying to solve.
 

1. What is the solution to ((2^n)+1)/(n^2)?

The solution to ((2^n)+1)/(n^2) is not a specific number, but rather a mathematical expression. It is equal to (2^n)/(n^2) + 1/(n^2).

2. Is there a simplified form for ((2^n)+1)/(n^2)?

Yes, the expression can be simplified to (2^n)/(n^2) + 1/(n^2) = 2^n/(n^2) + 1/(n^2) = (2^n + 1)/(n^2).

3. Can ((2^n)+1)/(n^2) be written as a single term?

No, ((2^n)+1)/(n^2) cannot be written as a single term as it is a sum of two terms (2^n)/(n^2) and 1/(n^2).

4. Is the solution to ((2^n)+1)/(n^2) always positive?

It depends on the value of n. If n is a positive integer, then the solution will be positive. However, if n is a negative integer, the solution will be negative.

5. How can ((2^n)+1)/(n^2) be used in real-life situations?

This expression may arise in various mathematical and scientific calculations, such as in the study of exponential growth or in the analysis of algorithms. It may also be used in computer science and engineering to optimize and analyze code performance.

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