pre-algebra
Name:
maksim rukov
School:
Московский государственный университет имени М. В. Ломоносова
About:
I am a fifteen year old Russian student, and I love mathematics with all my heart. I hope God grants me the honor of contributing to this stupendous field as much as I can. I am interested in number theory and real analysis.
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Questions Asked
pre-algebra:
Group Title
Given \(g_n:[0,1]\to\mathbb{R}\) and \(g:[0,1]\to\mathbb{R}\), assume that there is a number \(M\) such that \(|g_n(x)\leqslant M|\) for all…
updated 2 years ago
4 replies
1 Medal
Mathematics
pre-algebra:
Group Title
This question is inspired from this one: http://openstudy.com/study?login#/updates/4fa7f4e2e4b059b524f3bb68
How could one prove that \(\s…
updated 2 years ago
3 replies
2 Medals
Mathematics
pre-algebra:
Group Title
A professor asked me the following question:
"Is \(2\) a primitive root \((\text{mod }15)\)? Explain."
…
updated 2 years ago
3 replies
2 Medals
Mathematics
pre-algebra:
Group Title
Is there a formal way to show that \(\mathbb{Z}_{4}\) and \(\mathbb{U}_{10}\) are isomorphic? For the record,\[\mathbb{Z}_{4}=\{[0],[1],[2],…
updated 2 years ago
2 replies
1 Medal
Mathematics
pre-algebra:
Group Title
So, our professor just returned us our test, and I got all questions correct except for one:
"Solve for \(x\):\[24=16x-40"\]I don't get i…
updated 2 years ago
14 replies
2 Medals
Mathematics
pre-algebra:
Group Title
Our mentor just gave us a test, and in it, there was a question that asked the following:
"Show that \(\mathbb{Z}_6\) is not isomorphic to …
updated 2 years ago
6 replies
1 Medal
Mathematics
pre-algebra:
Group Title
I ran into the following exercise:
Define \(f:(0,c)\to\mathbb{R}\), for some \(c\in\mathbb{R}\) with \(0<c<\infty\), by\[f(x)=x^2.\]Then \(…
updated 2 years ago
12 replies
2 Medals
Mathematics
pre-algebra:
Group Title
It is too long.
updated 2 years ago
11 replies
2 Medals
Mathematics
pre-algebra:
Group Title
Let\[L(x)=\int_{1}^{x}\frac{dt}{t}.\]How can I show that there is a unique number \(e\), such that\[L(e)=\int_{1}^{e}\frac{dt}{t}=1?\]
updated 2 years ago
9 replies
3 Medals
Mathematics
pre-algebra:
Group Title
Let\[L(x)=\int_{1}^{x}\frac{1}{t}dt.\]How can I show that\[L(ab)=L(a)+(b)?\]
updated 2 years ago
15 replies
2 Medals
Mathematics
pre-algebra:
Group Title
How can I show that \(x_1=[a_0;a_1,a_2,\dots]\) is equivalent to \(x_2=[a_1;a_2,a_3,\dots]\)?
updated 2 years ago
6 replies
3 Medals
Mathematics
pre-algebra:
Group Title
How can I use Euler's generalization of Fermat's little theorem to compute\[18!\text{ }(\text{mod }437)?\]
updated 2 years ago
4 replies
1 Medal
Mathematics
pre-algebra:
Group Title
If \(p\) is prime and \(x^2\equiv1\text{ }(\text{mod }p)\), then \(x\equiv\pm1\text{ }(\text{mod }p)\).
\(\text{Proof.}\) Let \(p\) be prim…
updated 2 years ago
9 replies
3 Medals
Mathematics
pre-algebra:
Group Title
How many different combinations of Rubik's cube are there, and how can you calculate them?
updated 2 years ago
2 replies
No Medals Yet
Mathematics
pre-algebra:
Group Title
i'd like to know if there's a way to change a username. i didn't know i'd grow tired of this one.
updated 2 years ago
1 reply
3 Medals
Mathematics
pre-algebra:
Group Title
@TuringTest, @across, @JamesJ: do you know what is a good book to better my understanding of real analysis?
updated 2 years ago
2 replies
No Medals Yet
Mathematics
pre-algebra:
Group Title
Prove that\[\left(m^{(p-1)(q-1)}\right)^km\equiv m\text{ }(\text{mod }pq),\]where \(m<pq\), \(\gcd(m,pq)\neq1\), \(p\) and \(q\) are primes,…
updated 2 years ago
2 replies
4 Medals
Mathematics
pre-algebra:
Group Title
Simplify\[\frac{P^{ab}P}{P^{a}P^{b}}\text{ }(\text{mod }ab)\]
updated 2 years ago
4 replies
2 Medals
Mathematics
pre-algebra:
Group Title
Could somebody explain to me what is an isomorphism and give me an example? I'm not looking for a Wikipedia definition, but rather a persona…
updated 2 years ago
7 replies
3 Medals
Mathematics
pre-algebra:
Group Title
I need a pedagogical exercise of the application of the Weierstrass \(M\)-test. Anyone?
updated 2 years ago
19 replies
6 Medals
Mathematics
pre-algebra:
Group Title
I take these words back.
updated 2 years ago
1 reply
3 Medals
Mathematics
pre-algebra:
Group Title
Nobody knew the answer to this one.
updated 2 years ago
1 reply
1 Medal
Mathematics
pre-algebra:
Group Title
Is there a function that resembles the \(\text{sqrt}\) function but whose limit as \(x\to\infty\) exists?
updated 2 years ago
6 replies
2 Medals
Mathematics
pre-algebra:
Group Title
x+5=8 find x
updated 2 years ago
15 replies
2 Medals
Mathematics
pre-algebra:
Group Title
How can I find the least primitive root of \(10007\)?
This is number theory.
updated 2 years ago
4 replies
1 Medal
Mathematics
pre-algebra:
Group Title
Can somebody tell me how the Taylor expansion of\[\ln\left(\frac{x}{n}+1\right)=\frac{x}{n}-\frac{x^2}{2n^2}+\frac{x^3}{3n^3}-\cdots?\]
Acc…
updated 2 years ago
13 replies
1 Medal
Mathematics
pre-algebra:
Group Title
I am trying to show that for every \(\epsilon>0\), there exists an \(N\in\mathbb{N}\) such that\[\left|\left(\frac{x}{n}+1\right)^n-e^x\righ…
updated 2 years ago
4 replies
1 Medal
Mathematics
pre-algebra:
Group Title
@amistre64 Show that\[t-\frac{t^2}2\leq \ln(1+t)\leq t\]for \(t>-1\). Do you know how I can do this?
updated 2 years ago
9 replies
3 Medals
Mathematics
pre-algebra:
Group Title
This is a ghost thread.
updated 2 years ago
No Medals Yet
Mathematics
pre-algebra:
Group Title
Let \(m_1\), \(m_2\), ..., \(m_k\) be pairwise relatively prime, \(M=m_1m_2\cdots m_k\), \(M_1=M/m_1\), \(M_2=M/m_2\), ..., \(M_k=M/m_k\), a…
updated 2 years ago
2 replies
1 Medal
Mathematics
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