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For questions about factorization, the decomposition of mathematical objects (e.g. natural numbers, polynomials) into products of smaller objects (e.g. primes, lower degree polynomials).
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Can nonnegative functions $f(x,y,z)$ be written as a product of pairwise functions $u(x,y) v...
Let $f(x,y,z)=x^2+y^2+z^2$ for $(x,y,z) \in \mathbb{R}^3$. The only zero of $f$ is $(0,0,0)$.
If we had three functions $u,v,w$ such that $f(x,y,z)=u(x,y)v(y,z)w(z,x)$ for every $(x,y,z) \in \mathbb{R …