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Zara
  • Member for 4 years, 1 month
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5 votes
1 answer
1k views

What is $\det(A + I)$ when $AA^t = I$ and $\det(A) < 0$?

5 votes
0 answers
124 views

Proving that $\sum_{n = 1}^\infty 2^{-4^n}$ is transcendental

4 votes
2 answers
155 views

Proving the identity of $\sum_{k = 0}^n{4n \choose 4k} = 2^{4n - 2} + (-1)^n2^{2n - 1}$ combinatorially

3 votes
1 answer
112 views

Showing that these algebras are isomorphic

3 votes
1 answer
101 views

$x^3 - 6 = 25y^2 + 35y$ has no non-zero integer solutions [duplicate]

3 votes
2 answers
404 views

Showing that $\mathrm{Hom}_R(R/I, M) \cong \mathrm{Ann}_I(M)$

3 votes
3 answers
141 views

Proving that ${n \choose 1} - 2{n \choose 2} + 3{n \choose 3} + \dots + (-1)^{n - 1}n{n \choose n} = 0$

2 votes
1 answer
296 views

Showing that a certain map in a commutative diagram with exact rows is injective

2 votes
0 answers
51 views

Finitely generated subgroups of $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$

2 votes
1 answer
129 views

Proving that $T + S: V \rightarrow V$ is the identity transformation when $N(T) \subseteq R(S)$ and $R(T) \subseteq N(S)$ and $T^2v = Tv, \ S^2v = Sv$

2 votes
1 answer
110 views

There is a number field $L$ over $K$ where all ideals of $\mathbb{Z}_K$ are principal in $\mathbb{Z}_L$

2 votes
2 answers
213 views

Fundamental units of $\mathbb{Q}(\sqrt[3]{12})$

1 vote
0 answers
39 views

Proving the identity $\sum_{i=0}^n{n + i \choose i}\frac{1}{2^i} = 2^n$ combinatorially [duplicate]

1 vote
2 answers
76 views

Listing numbers $1$ to $10$ such that only one number is smaller than its neighbours

1 vote
1 answer
84 views

Proving the identity $\sum_{k = r}^n {n \choose k}{k \choose r}2^k = {n \choose r}2^r3^{n - 2}$

1 vote
2 answers
111 views

Proving the identity $\sum_{k = 1}^nk^2 {n \choose k}^2 = n^2{2n - 2 \choose n - 1}$ combinatorially

1 vote
2 answers
66 views

Proving ${n + 2 \choose m + 1} = {n \choose m + 1} + 2{n \choose m} + {n \choose m - 1}$ using the Binomial Theorem [duplicate]

1 vote
0 answers
66 views

How to identify the two copies of $D_{24}$ in the homomorphisms of the 2 musical actions?

1 vote
1 answer
242 views

Finding base for a subspace of cubic polynomials with derivative equal to zero in a specific point

1 vote
2 answers
94 views

Proving that the subset of all linear transformations from $\mathbb{R}^5$ to $\mathbb{R}^4$ where $n(T) > 2$ is not a subspace

0 votes
1 answer
69 views

Finding base for subspace of cubic polynomials with vanishing integrals

0 votes
1 answer
612 views

Showing that $p$ is a Fermat prime if and only if every quadratic non-residue mod $p$ is also a primitive root mod $p$ [duplicate]

0 votes
1 answer
61 views

Showing that matrix $A$ and linear operator $T: M_{n\times n} \rightarrow M_{n\times n}$ ($T(B) = AB$) have the same eigenvalues

0 votes
0 answers
58 views

Writing $\cos(\frac{m}{n}\pi)$ in terms of roots of unity

0 votes
1 answer
51 views

Retrieving second order ODE from its solutions

0 votes
0 answers
69 views

Every number field of degree $3$ is of the form $\mathbb{Q}(\alpha)$ where $\alpha$ has minimal polynomial $x^3 + ax + b$