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If p, q are positive integers, f is a f...

If p, q are positive integers, f is a function defined for positive numbers and attains only positive values such that `f(xf(y))=x^p y^q`, then prove that `p^2=q`.

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To prove that \( p^2 = q \) given the functional equation \( f(xf(y)) = x^p y^q \), we will follow these steps: ### Step 1: Analyze the given functional equation We have the equation: \[ f(xf(y)) = x^p y^q \] This equation holds for all positive integers \( x \) and \( y \). ...
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