How to prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational roots?
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
141093
How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
18702
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
52960
Show that the curve $x^2+y^2-3=0$ has no rational points
55197
Roots of $ x^3-3x+1$
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
81854
Prove $x^4 + 131 = 3y^4$ has no integer solutions
107089
finding rational roots of polynomials
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
106011
Proving it has all real roots
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
85383
No. Of real roots of an equation
30511
Monic $f(x)\in\Bbb Z[x]$ has no rational root if $f(0)\ \&\ f(1)$ odd [Parity Root Test, Modular Root Test]
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer