If the coefficients of a quadratic equation are odd numbers, show that it cannot have rational roots
132931
Determining the parity of the coefficients of a quadratic given that there is a rational solution
100862
Polynomials with rational zeros
141184
Proof that a degree 4 polynomial has at least two roots
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
105679
Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients?
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
1190
Square Root of Rational Number $\frac{A}{B}$
131289
Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$
123441
Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
99502
Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$
113359
Proving that $x^2 + 4$ is not divisible by $3$
115241
If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$.
92537
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
117484
Why is $c+q$ still a primitive root modulo $q$?
55206
Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square