All Questions
7
questions
5
votes
0
answers
305
views
Valid Elementary Proof of the Bertrand-Chebyshev Theorem/Bertrand's Postulate? [closed]
$\textbf{Theorem}$ (Bertrand-Chebyshev theorem/Bertrand's postulate): For all integers $n\geq 2$, there exists an odd prime number $p\geq 3$ satisfying $n<p<2n$.
$\textit{Proof }$: For $n=2$, we ...
- 445
1
vote
1
answer
113
views
Elements of the sequence have a prime factors an element of the sequence
I am reading the following problem:
For the sequence $T=3, 7, 11, 15, 19, 23, 27 ...$ prove that every
number in $T$ has a prime factor that is also in $T$
My approach:
The sequence is of the form $...
- 1,609
2
votes
0
answers
37
views
Prime inert in each subfields never occurs
Suppose you are working with $K=\mathbb{Q}[\sqrt{m},\sqrt{n}]$ and $K_1=\mathbb{Q}[\sqrt{m}],K_2=\mathbb{Q}[\sqrt{n}], K_3=\mathbb{Q}[\sqrt{k}]$ where $m,n$ are squarefree integers and $k = mn/gcd(m,n)...
- 1,078
0
votes
0
answers
214
views
Need help interpreting this formula for the number of Goldbach partitions
1: Formula for the number of Goldbach partitions.
Let $g\left(n\right)$ denote the number of Goldbach partitions of even integer $2n$:
$$g_{\left(n\right)}=\sum_{3\leq p\leq2n-3}\left[\pi\left(2n-p\...
- 1,282
0
votes
1
answer
1k
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Prime Factorization of $m^2$
If $m$ is a positive integer, explain why each prime in the prime factorization of $m^2$ must occur an even number of times.
I did a small proof, I was wondering what's a nice way to explain it aside ...
- 602
0
votes
0
answers
301
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Proof that for a given prime $a$, there are only finite many carmichael-numbers $N=abc$ with $b,c$ prime
Please check if the following proof that for every prime $a$, the number of
carmichael numbers $N=abc$ , where $b$ and $c$ are also prime, is finite,
is correct!
First of all, we have
$$a-1|abc-1$$
$$...
- 85.1k
4
votes
2
answers
227
views
The Conjecture That There Is Always a Prime Between $n$ and $n+C\log^2n$
Let $n$ be 113. Use $n+C\log^2n$ to find the next consecutive prime or at least approximately how far away it is. Will you show me how to work this out step by step to show me how to use this formula? ...
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