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7 votes
2 answers
182 views

showing that $G$ does not have an embedding in $GL_n(F)$ for any $n\ge 1$ and field $F$

7 votes
2 answers
292 views

prove that for any $|x|\leq 1$, $|f(x)|\leq 5/4$ [duplicate]

7 votes
1 answer
97 views

Prove that $\sum_{n=1}^\infty \dfrac{1}{\log_2(a_n)}$ converges.

6 votes
1 answer
180 views

surjective group homomorphism between $\mathbb{Z}^2$ and $\mathbb{Z}_{30}$

4 votes
2 answers
74 views

countable-to-one set cardinality

3 votes
1 answer
352 views

Carmichael lambda function proof

3 votes
3 answers
665 views

connected and path components

3 votes
1 answer
119 views

Prove that $a_n = \sum_{k=0}^{\lfloor n/2\rfloor} 1/(k+1) {2k\choose k} {n\choose 2k}$

3 votes
1 answer
255 views

determining whether a set is dense in $\mathcal{C}(D,\mathbb{C})$

3 votes
2 answers
131 views

isomorphism $\psi$ between quotient rings

3 votes
3 answers
214 views

Evaluating the limit $\lim\limits_{n\to\infty} \frac{2^{n^{k}}}{n!}$

3 votes
1 answer
153 views

equivalent definitions of prime ideals

3 votes
1 answer
117 views

Prove that $g(z)$ is identically zero

2 votes
1 answer
70 views

prove that $f^{-1}((0,0))$ is infinite

2 votes
1 answer
36 views

Prove that there exists $1\leq a < p^{1/(2\sqrt{e})} (\log p)^2$ that is a quadratic non-residue modulo p

2 votes
1 answer
207 views

Showing a set is dense in $C([0,1]\times [0,1])$

2 votes
0 answers
182 views

Proof of Picard's theorem

2 votes
2 answers
63 views

existence of certain continuous function $\overline{f}$

2 votes
1 answer
50 views

equivalent properties of cardinals

2 votes
1 answer
52 views

finite subsets proof

1 vote
2 answers
325 views

subgroup of $\mathbb{Z}_9 \times \mathbb{Z}_{15}$

1 vote
0 answers
159 views

Find all subgroups of the dihedral group $D_n$

1 vote
2 answers
130 views

non-equivalence of $p$-norms in $\ell_1$

1 vote
1 answer
68 views

completeness of metric space $C_b(X,Y)$

1 vote
0 answers
82 views

Prove that for any real numbers $x_1,\cdots, x_n, \sum_{i=1}^n \sum_{j=1}^n a_{ij} x_i x_j\ge 0$

1 vote
1 answer
48 views

Prove that for any real number $x, \sum_{i=1}^n a_i \lfloor ix \rfloor\ge 0$

1 vote
1 answer
70 views

Find all positive integers m so that for $n=4m (2^m - 1)$, $n | (a^m - 1)$ for all a coprime to n

1 vote
0 answers
65 views

Prove that $\sqrt[n]{a}\in \mathbb{Q}$ [duplicate]

1 vote
0 answers
36 views

Prove that ${n\choose k}$ has at least k distinct prime divisors by proving an intermediate statement first

1 vote
0 answers
52 views

Prove that $a_n=a_{n-1}$ [duplicate]