Show that there is no rational number whose square is $2$ or $8$
6275
How can you prove that the square root of two is irrational?
75012
Additive group of rationals has no minimal generating set
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
85895
Proving all rational numbers including negatives are countable
24706
Is there a rational number between any two irrationals?
19954
Perfect set without rational numbers
96647
Number theory: Problem involving rational numbers
101169
Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$
150576
When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$?
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
84379
Prove that there is no integer a for which $a^2 - 3a - 19$ is divisible by 289
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
67161
No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
139979
Proof there is a rational between any two reals