query: Entire function $f(\frac{1}{p})=\frac{1}{1+p}$ for all prime $p$.
positive_passages.docid: 150124
positive_passages.text: Holomorphic function such that $f(\frac{1}{n})=\frac{1}{n+1}$.
negative_passages.docid: 120147
negative_passages.text: For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
negative_passages.docid: 145956
negative_passages.text: $f$ is entire without any zeros then there is an entire function $g$ such that $f=e^g$
negative_passages.docid: 103340
negative_passages.text: Show that this entire function is polynomial.
negative_passages.docid: 37871
negative_passages.text: Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
negative_passages.docid: 155531
negative_passages.text: Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
negative_passages.docid: 82836
negative_passages.text: If $f$ is an entire function with $|f(z)|\le 100\log|z|$ and $f(i)=2i$, what is $f(1)$?
negative_passages.docid: 68221
negative_passages.text: Question regardles primes and the fundamental theorem of arithmetic
negative_passages.docid: 126931
negative_passages.text: Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
negative_passages.docid: 44600
negative_passages.text: How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
negative_passages.docid: 140949
negative_passages.text: Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
negative_passages.docid: 105172
negative_passages.text: Prove that the entire function is constant over certain conditions.
negative_passages.docid: 2527
negative_passages.text: Entire function bounded by a polynomial is a polynomial
negative_passages.docid: 133837
negative_passages.text: Entire function dominated by another entire function is a constant multiple
negative_passages.docid: 26126
negative_passages.text: $f \in L^1$, but $f \not\in L^p$ for all $p > 1$
negative_passages.docid: 39073
negative_passages.text: Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
negative_passages.docid: 133427
negative_passages.text: analytic function on $\mathbb{C}$ such that $f\Bigl(\frac{1}{2n}\Bigr)=f\Bigl(\frac{1}{2n+1}\Bigr)=\frac{1}{2n}$