if $X^2 +AX+B=0$ has a rational root, prove it is an integer.
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
47949
If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
107089
finding rational roots of polynomials
13656
Prove existence of a real root.
126445
Proving the second root of a quadratic equation
92701
let $a,b,c \in\mathbb{R} ,a<3$ and all roots $p(x)=x^3+ax^2+bx+c=0$ be negative . then prove that $b+c\neq 4$
130300
Proof that every quadratic residue has two roots, modulo a prime
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
103165
the number of the positive integer numbers $k$ that makes for the two quadratic equations $ \pm x^2 \pm px \pm k$ rational roots.
152167
Prove that if $x,y,z$ are integers such that $x^2+y^2=z^2$, then $xyz \equiv o \pmod{60}$.
11664
If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$
86882
Proving Gauss' polynomial theorem (Rational Root Test)
51649
prove there is no smallest positive rational number
6275
How can you prove that the square root of two is irrational?
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution