Prove that there is no non-constant polynomial $P(x)$ with integer coefficients such that $P(n)$ is a prime number for all positive integers $n$.
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
126494
Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
59261
If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.
38419
Existence of Polynomial with whom product contains only prime powers
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
69523
Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
21862
Proof of lack of pure prime producing polynomials.
131289
Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
151729
Existence of a unique polynomial
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
132165
"Polynomials" with non-integer exponents
99000
No polynomial with integer coefficients satisfies the conditions
94682
Polynomial: prove there is no double root