Find all positive integers c such that it is possible to write c = a/b + b/a

In summary, the equation for finding all possible values of c is c = a/b + b/a, where a and b are positive integers. There are infinitely many solutions for this equation, and a and b can be equal, resulting in c = 2. There are no restrictions on the values of a and b, and to find all possible values of c, a combination of trial and error and mathematical techniques can be used, such as factoring and determining the greatest common factor.
  • #1
Derivative86
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Find all positive integers c such that it is possible to write c = a/b + b/a with positive integers a and b.
Please help me :smile:
 
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  • #2
You know [tex]c=\frac{a^2+b^2}{ab}[/tex] is an integer, so [tex]ab[/tex] divides [tex]a^2+b^2[/tex]. What factors must a and b have in common?
 
  • #3
i got c=2 as the answer, is it right?
 
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1. What is the equation for finding all possible values of c?

The equation is c = a/b + b/a, where a and b are positive integers.

2. How many solutions are there for the equation c = a/b + b/a?

There are infinitely many solutions for this equation.

3. Can the values of a and b be equal?

Yes, a and b can be equal, which would result in c = 2.

4. Are there any restrictions on the values of a and b?

No, a and b can be any positive integers.

5. How can I find all possible values of c?

To find all possible values of c, you can use a combination of trial and error and mathematical techniques, such as factoring and determining the greatest common factor.

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