query: prove that if $ h = |f_1|^2 \cdots + |f_n|^2$ is constant then $f_i$ is constant
positive_passages.docid: 10194
positive_passages.text: If $f,g$ are analytic in the unit disk, and $|f|^2+|g|^2=1$, then $f,g$ constant.
negative_passages.docid: 3818
negative_passages.text: Proving two entire functions are constant.
negative_passages.docid: 56978
negative_passages.text: How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
negative_passages.docid: 97371
negative_passages.text: Proving a function is constant, under certain conditions?
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 75653
negative_passages.text: Prove that $|f ''|\ge 4$
negative_passages.docid: 48275
negative_passages.text: $f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
negative_passages.docid: 74202
negative_passages.text: Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$.
negative_passages.docid: 96894
negative_passages.text: Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
negative_passages.docid: 63836
negative_passages.text: Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
negative_passages.docid: 86517
negative_passages.text: If $|f(z)|\le |g(z)|$, can we say $f$ is constant?
negative_passages.docid: 32789
negative_passages.text: Show bounded harmonic function on $\mathbb{C}$ is constant.
negative_passages.docid: 100987
negative_passages.text: Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
negative_passages.docid: 4498
negative_passages.text: Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
negative_passages.docid: 62254
negative_passages.text: Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
negative_passages.docid: 55742
negative_passages.text: Showing that $f_{2n+1}=f_{n+1}^2+f_n^2$.
negative_passages.docid: 64650
negative_passages.text: If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant