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Significance of derivative in finding square free decomposition
If $gcd(f(x),`f(x))=1$ then f(x) is square free. But what is the reason behind taking derivative of f(x)? How one came to this conclusion?
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A question on polynomials.
Let a polynomial $f\in\mathbb{R}[x,y]$, and
$f(x,y)=(x^2+y^2)p(x,y)^2-q(x,y)^2$ and $p,q$ are coprime to each other.
When do, $f$ and $\frac{{\partial f}}{{\partial x}}$ and $\frac{{\partial f}}{{\...
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