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Jan
21
answered If $3^x$ and $5^x$ are both integers, is $x$ an integer?
Jan
21
comment The convergence of $\sum_{n=2}^{\infty} {1\over \ln(n!)}$
The divergence of the $1/n\log n$ series can be seen with Cauchy's condensation test (which can be proven with elementary tools).
Jan
21
comment If $3^x$ and $5^x$ are both integers, is $x$ an integer?
Related: mathoverflow.net/questions/17560/…
Jan
19
awarded  Necromancer
Jan
9
comment Mistake in Spivak's *Calculus on Manifolds*?
There is indeed a mistake in this exercise. If I recall correctly, he originally meant $\lambda_i$ instead of $|\lambda_i|$. This is a related question.
Dec
28
comment Relation between norm and determinant of a linear operator
Saying the obvious, the matrix $\begin{pmatrix} 1 & -1 \\ 1 & 0 \end{pmatrix}$ has determinant $1$ and it does not preserve norms as the identity matrix does. What do you mean by "present the norm as the determinant"?
Dec
28
comment Two questions about divisible
A hint on 1) is $\varphi(10)=4$.
Dec
22
awarded  Constituent
Dec
14
comment Question about proving $\displaystyle\lim_{n\to\infty} n=\infty$ using the limit definition for a converging sequence
This argument only shows the limit is not converging to a real number. The sequence $(1,-1,1,-1,...)$ also does not converge to any real number, and $\lim\limits_{k\to\infty} (-1)^k\neq\infty$.
Dec
12
comment How do I prove that $x^s=(-1)^k \sum_{k=0}^{(r-1)/2}\binom{r}{2k}p^{s(r-2k)}$ has no solutions?
The sum is $\Re (p^s+i)^r$.
Dec
12
comment How do I prove that $x^s=(-1)^k \sum_{k=0}^{(r-1)/2}\binom{r}{2k}p^{s(r-2k)}$ has no solutions?
Is $(-1)^k$ inside the sum?
Dec
11
comment Find Solutions To Some Diophantine Equations
The diophantine equation $a(a+b+c)=nbc$ is equivalent to $$a^2(1/n+1/n^2)=(b-a/n)(c-a/n).$$
Dec
8
awarded  Caucus
Dec
8
comment Simple second order differential equation of the form $f''(x)+ h(x) = 0$
$a$ is a function of time. To compute the position, you need $a(1)$ and some basic geometry.
Dec
8
comment Simple second order differential equation of the form $f''(x)+ h(x) = 0$
Use $\sin(a)\approx a$ and get a second-order linear differential equation. Find the solution using the contour conditions and give it as an approximate answer.
Dec
5
answered Inverse of $f(x) = \sum_{i=0}^x \lfloor 2 \pi i \rfloor$
Nov
29
revised Conjecture about the powers of 2 in the prime factorizations of the series $a_n = n(n+1)(n+2)$
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Nov
29
revised Conjecture about the powers of 2 in the prime factorizations of the series $a_n = n(n+1)(n+2)$
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Nov
29
revised Conjecture about the powers of 2 in the prime factorizations of the series $a_n = n(n+1)(n+2)$
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Nov
29
answered Conjecture about the powers of 2 in the prime factorizations of the series $a_n = n(n+1)(n+2)$