Prove that $2c^3+1$ is never a perfect cube for $c \in \mathbb{N}^*$
34942
solving $x^3-2y^3=1$ using cubic number field
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
94958
Prob. 6 (d), Chap. 1, in Baby Rudin, 3rd ed: How to complete this proof?
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
149071
Let $d$ be any positive integer not equal to $2, 5,$ or $ 13$ , then $\exists a, b \in \{2, 5, 13, d\}$ such that $ab − 1$ is not a perfect square?
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
30568
Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$