ThEdArKlOrD

For fixed $\epsilon >0$, determine whether or not, there exist polynomial $P(x)\in \mathbb{R}[x]$ such that $|P(n)-p_n|<\epsilon$ where $p_n$ is $n^{th}$ prime numbers for all positive integer $n$

Define sequence $\{ a_n\}$ by $a_{n+3}=a_{n+2}+a_{n+1}-a_{n}$ for all $n\in \mathbb{Z}^+$
Find all $a_1,a_2,a_3$ such that $a_n$ is square of integer for all $n\in \mathbb{Z}^+$

Find all two variables polynomials $P(x,y)$ such that for any real numbers $a,b,c$, we have 

$P(ab,c^2-2)+P(ac,b^2-2)+P(bc,a^2-2)=0$

Here is Epsilon No. 8

Link; https://drive.google...EpTS0dka1E/view