query: Any chance for a solution of $f[f(x)]=x^2+1$?
positive_passages.docid: 144042
positive_passages.text: On the functional square root of $x^2+1$
negative_passages.docid: 95105
negative_passages.text: Solutions in complex number field, instead of $\mathbb{N}$, to Fermat's Last Theorem
negative_passages.docid: 56958
negative_passages.text: bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 132093
negative_passages.text: Solve $f(f(x))=f(x)$
negative_passages.docid: 124581
negative_passages.text: Solving $x^2 - 1 = e^x$
negative_passages.docid: 72769
negative_passages.text: How find this function $xf(x^2)=f(x),x>0$
negative_passages.docid: 105999
negative_passages.text: An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
negative_passages.docid: 60456
negative_passages.text: Find the power series of $f(x)=\frac{1}{x^2+x+1}$
negative_passages.docid: 24862
negative_passages.text: Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
negative_passages.docid: 49794
negative_passages.text: Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 42699
negative_passages.text: Solve for $f(x)$ if $f(f(x))=6x-f(x)$
negative_passages.docid: 64339
negative_passages.text: Find $f$ where $f'(x) = f(1+x)$
negative_passages.docid: 17154
negative_passages.text: Does a non-trivial solution exist for $f'(x)=f(f(x))$?
negative_passages.docid: 113045
negative_passages.text: How do I find the inverse of $f(x) = \frac{x}{x^2 + 1}$
negative_passages.docid: 133164
negative_passages.text: Rational solutions for $x^2+y^2=3$