If $x^2+ax+b=0$ has a rational root, show that the root is an integer.
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
157487
Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
90043
Show that if $r$ is an nth root of $1$ and $r\ne1$, then $1 + r + r^2 + ... + r^{n-1} = 0$.
3206
Given $ax^2+by^2+cxy > 0$, what can I deduce about $a$, $b$, and $c$?
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
117352
Show $x^n+ax+b=0$ has most two solutions
130300
Proof that every quadratic residue has two roots, modulo a prime
86882
Proving Gauss' polynomial theorem (Rational Root Test)
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
1190
Square Root of Rational Number $\frac{A}{B}$
148310
Showing rational numbers are algebraic
6582
Prove the existence of the square root of $2$.
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.