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BalsamicVinegar
  • Member for 5 years, 10 months
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5 votes
1 answer
310 views

Solve $x^{2} = -1$ in $\mathbb{Q}_{5}$.

3 votes
2 answers
82 views

Show : $(m,n)=1\implies(mx+ny,mn)=(m,y)(n,x)\;\forall x,y\in\mathbb Z$.

3 votes
2 answers
166 views

Show that $\sum_{d \mid n} (-1)^{\frac{n}{d}} \varphi(d) = 0$ for $n$ even.

2 votes
1 answer
185 views

Let $f(n) = \sum_{(k,n)=1} e^\frac{2\pi ik}{n}$. Show that $f(n) = \sum_{k=1}^{n}\left(\sum_{d\mid (k,n)} \mu(d)e^{\frac{2\pi ik}{n}} \right) $

2 votes
2 answers
327 views

Finding the lim inf and lim sup of a sequence

2 votes
3 answers
86 views

Proving that a sequence converges if $|a_n - a_{n+1}| < Mr^n$ for some $M > 0$ and $r \in (0,1).$

1 vote
1 answer
64 views

Find a function $f(x)$ which is defined at every real number but is continuous at $0$ and is not continuous at every other number [duplicate]

1 vote
3 answers
29 views

Finding a Set Which Spans a Given Set

1 vote
2 answers
67 views

Proving the supremum of a set

1 vote
1 answer
100 views

For which $t \in \mathbb{N}$ does $\varphi(t) \mid t$? [duplicate]

1 vote
2 answers
59 views

Convergence of $\frac{z^{n}}{n}$ in $\mathbb{C}$

1 vote
1 answer
40 views

Prove that $a^{b} \equiv 3 \,( \text{mod}\, 4)$ implies $a,b$ odd.

1 vote
1 answer
58 views

Verification of proof of convergence in $p$-adic fields

1 vote
0 answers
49 views

Can you apply the Residue Theorem to real domains?

0 votes
0 answers
18 views

Multivariable Optimization of Microbes

0 votes
1 answer
342 views

Show that $\frac{1}{\zeta(s)} = \sum_{n=1}^{\infty} \frac{\mu(n)}{n^{s}}$.

0 votes
1 answer
41 views

Prove that $\frac{\pi(2x)\text{log}\, x}{x}$ has a constant upper bound.

0 votes
2 answers
47 views

Sum over all characters $\chi$ mod $m$

0 votes
1 answer
234 views

Let there be a sequence such that the distance between two consecutive terms converges to 0. Must this sequence converge? [duplicate]

0 votes
2 answers
43 views

Verification of proof of nonconvergence

0 votes
1 answer
74 views

Proving a Linear Transformation

0 votes
1 answer
32 views

Proving an Inequality with the Mean Value Theorem

0 votes
2 answers
39 views

Proving $f(x) \ge 1+x$ if $f'$ increasing and $f(0)=f'(0)=1$

0 votes
2 answers
41 views

Let $\{a_n\}_n$ be a sequence and suppose $\{a_n\}_n$ isn't bounded above. Prove that there's a subsequence $\{a_{n_k} \}_k$ such that $a_{n_k} → ∞.$

-1 votes
2 answers
44 views

If $f$ is entire and $f(3/n) = 6- \frac{10}{n} - \frac{20}{n^2}$, then find $f$ in explicit form.