Prove that if $p$ and $q$ are odd numbers then $x$ is not a rational number in $x^2 + 2px +2q=0$
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
30478
How to prove that a number is irrational
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
18633
Prove every odd integer is the difference of two squares
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
143733
Is this proof that $\sqrt 2$ is irrational correct?
101162
Square root of $2$ is irrational
96341
Proving $v(s,p)=2^{p-1}(2s-1)$ is a bijection of natural numbers and $f(s)=2s-1$ is a bijection between natural numbers and odd numbers.
125267
Prove that $2^{1/2}$ is irrational
155886
let q be an odd prime and p a prime dividing $1+n+\dots+n^{q-1}$
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
31744
Proving that there is an irrational number between any two unequal rational numbers.
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
54359
Odd Primes Problem Proof
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]