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anemone
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Find all positive integers $n$ for which the equation $(x^2+y^2)^n=(xy)^{2014}$ has positive integer solutions.
anemone said:Find all positive integers $n$ for which the equation $(x^2+y^2)^n=(xy)^{2014}$ has positive integer solutions.
A positive integer solution is a set of values for the variables in an equation that result in a positive integer answer.
The number of positive integer solutions for this equation is infinite.
Yes, it is possible for $x$ and $y$ to be non-integer values and still satisfy the equation, as long as the result is a positive integer.
The powers $n$ and $2014$ do not have a specific relationship in this equation. They are both simply used as exponents to represent the equation.
Yes, there are some patterns and strategies that can be used to find positive integer solutions for this equation, such as factoring and using modular arithmetic. However, there is no guarantee that these strategies will work for all cases.