Prove there is no rational number whose cube is $13$
97071
Is the cube root of a prime number rational?
23301
There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
69039
Prove that $2730$ divides $n^{13} - n$ for all integers $n$.
113695
Show that there is no integer n with $\phi(n)$ = 14
3208
There is no smallest rational number greater than 2
75012
Additive group of rationals has no minimal generating set
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
59365
Why isn't $ SA_{\text{cube}} = 3x^2 $?
92672
Number of elements which are cubes/higher powers in a finite field.
30478
How to prove that a number is irrational
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
12701
Perfect set without rationals
86233
A $3 \times 3 \times 3$ cube has no Hamiltonian path starting at the corner.
18360
Proof that the irrational numbers are uncountable
113359
Proving that $x^2 + 4$ is not divisible by $3$
99037
Prove the sum of all numbers that do not have a multiplicative inverse mod $n$