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pureundergrad
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5 votes
1 answer
121 views

Roots of $x^8-3$ over $GF(17)$

5 votes
1 answer
2k views

Explicitly calculate shape operator for graph of $f(x,y)=xy$

5 votes
4 answers
526 views

$p \geq 5$ prime. $2p+1$ not a prime. Then $\phi(n)=2p$ has no solution.

4 votes
1 answer
156 views

Galois group of $(x^3-2)(x^5-1)$ over $\mathbb{Q}$.

4 votes
2 answers
381 views

Group of order $p^{\alpha}q$ is not simple.

3 votes
1 answer
81 views

Is there a distance on $\mathbb{R}$ so that a non-empty subset is open iff its complement is finite? [duplicate]

3 votes
0 answers
358 views

Explicit parametrization for a 3-ellipse? A 4-ellipse?

3 votes
0 answers
102 views

Is $[-1,1]\times [-1,1]$ a compact subset of $\mathbb{R}^{2}$ with respect to this distance?

3 votes
2 answers
2k views

Show that the ideal $I = (2,1+\sqrt{-13})$ is a maximal ideal in $\mathbb{Z}[\sqrt{-13}]$? Is it principal?

2 votes
2 answers
2k views

Show that $4\mathbb{Z}$ is maximal in $2\mathbb{Z}$.

2 votes
3 answers
128 views

Show $f$ is not differentiable at $x = 0$.

2 votes
1 answer
235 views

Prove that this metric space is compact.

2 votes
2 answers
45 views

Is there a distance $d$ such that the metric topology on $\mathbb{R}$ is this set of symmetric intervals

2 votes
2 answers
51 views

Is there a distance on $\mathbb{R}$ with this property? (compactness)

2 votes
4 answers
124 views

$x^3+2x+2 \in \mathbb{F}_3[x]$. Let $\alpha$ be a root in some extension field.

2 votes
1 answer
415 views

Winding number always zero by definition. Help find the mistake.

2 votes
2 answers
224 views

Group of order $60$ with $20$ elements of order $3$

1 vote
1 answer
138 views

Schwarz's lemma application on a composition of functions

1 vote
1 answer
301 views

When is $\sigma(n)=28$?

1 vote
1 answer
139 views

$\omega$ is the $11$th primitive root of unity. Find minimal polynomial of $\beta=\omega+\omega^3+\omega^4+\omega^5+\omega^9$

1 vote
1 answer
54 views

Laurent series of $f(z)=\frac{z-1}{z(z^3-1)}$ for $0<|z|<1$ and $|z|>1$.

1 vote
2 answers
3k views

Determine size or number of jordan blocks

1 vote
2 answers
34 views

Let $\alpha=\sqrt[5]{2}+\sqrt{5}$, show that $\sqrt{5}\in\mathbb{Q}(\alpha)$. [closed]

1 vote
3 answers
401 views

Minimal polynomial of $\alpha+i$ over $\mathbb{Q}$

1 vote
2 answers
82 views

What are the elements of $\mathbb{Z}_{2}[x]/I$? Is it a field?

0 votes
3 answers
64 views

For which value of $\delta$ is $\sum_{n=1}^{\infty}\frac{x}{n(1+n^{\delta}x^{2})}$ uniformly convergent on $\mathbb{R}$?

0 votes
0 answers
28 views

Explanation of a step in proof of Triangle Inequality for Contour Integrals

0 votes
2 answers
565 views

Corollary of Liouville's Theorem

0 votes
2 answers
126 views

$N$ and $M$ are normal subgroups, whose sizes are coprime. Show $|MN|=|M||N|$

0 votes
0 answers
70 views

What is the number of homomorphisms from $\mathbb{Z}_{10}\times \mathbb{Z}_{25}\to S_4$?