Show that there is no rational number such that $x^2=3$
109953
How to prove that $\sqrt 3$ is an irrational number?
113359
Proving that $x^2 + 4$ is not divisible by $3$
87764
Prove that the difference between two rational numbers is rational
32516
show that rational numbers with the multipiciation are not abelian finitely generated group
69902
$3$ never divides $n^2+1$
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
31744
Proving that there is an irrational number between any two unequal rational numbers.
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
69874
Are there any integer solutions to $a^3=b^2$?
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
87410
Are there real numbers that are neither rational nor irrational?
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
148243
Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.