9,367 reputation
2731
bio website
location
age 38
visits member for 2 years, 6 months
seen 24 mins ago

56m
comment What is the chromatic index of a complete graph with its edges doubled?
What does connectivity have to do with chromatic index?
15h
comment Best score in this puzzle
@DanielV The probability that $25$ integers have some common factor is $1 - 1/\zeta(25) = 1 - \prod_p (1 - p^{-25})$, but if you think about how quickly the terms $p^{-25}$ drop off, this is almost identical to $2^{-25}$ anyway.
21h
comment Best score in this puzzle
en.wikipedia.org/wiki/Hungarian_algorithm
1d
comment A question on the prime number theorem as presented in the following paper
The paper doesn't say anything to contradict this. You claim in your question that the paper says only $B$ can be taken arbitrarily close to $1$. Where does it say this?
1d
comment Remarks on a Previous Post
@HTFB You are thinking of Littlewood's phenomenon. No, that's for the much more precise approximation $Li(x)$. The approximation $\pi(x) \approx x/\ln x$ is off by a significant quantity (about $2x/\ln^2 x$) that doesn't change sign infinitely often.
1d
comment A question on the prime number theorem as presented in the following paper
The paper states that we can take $A=1$. Are you trying to say that "$A$ arbitrarily close to $1$" is an improvement over $A=1$?
2d
comment Demystifying the asymptotic expression for the partition function
@DietrichBurde That is a great reference. I'm a little confused though: did Erdős prove an asymptotic for $p(n)$ (as seemingly claimed in Nathanson), an asymptotic-with-unknown-constant for $p(n)$ (as it claims in Erdős here), or an asymptotic for $\log p(n)$ (in the style of the main theorem of Nathanson)?
2d
comment Palindromic Hypotenuses?
Why couldn't you get the right answer with Java? And how do you know what the right answer is?
2d
answered Palindromic Hypotenuses?
Oct
22
comment If $(a^2+b^2) \mid (c^2+d^2)$ and $\gcd(a,b)=\gcd(c,d)=1$ and $\gcd(a,c)>1$, what can be said about the components?
Why couldn't $c=2a, d=2b$? Are you missing some conditions??
Oct
21
answered Compute a multiple integral$\iint_{[0,1]^2} (xy)^{xy} dxdy$
Oct
21
comment Proof of $p_n<n^2$ by Elementary Means
@user170039 Chebyshev already proved something of the strength $p_n \le (1.2 + o(1)) n \log n$; this was nearly 50 years before PNT was established. The proof that karvens refers to is probably the simpler one due to Erdős.
Oct
21
comment Last 3 digits of $7^{12341}$
@rsadhvika $7 \equiv -1 \pmod 8$ so it is easy to see that any even exponent satisfies the $2$-adic part of the congruence. For the $5$-adic part, we easily observe that $7^2 = 49 \equiv -1 \pmod{25}$, so then $7^4 \equiv 1 \pmod{25}$, and an easy application of binomial theorem shows that $(7^4)^5 \equiv 1 \pmod{125}$.
Oct
21
comment Convergence/Divergence of the series $\sum\limits_{n=1}^{\infty}\tan(1/n)$
"for small nonnegative $x$"
Oct
21
answered On the difference between consecutive primes
Oct
20
comment A general solution for a (x+y)^n = x^n + y^n
If both $(x,y)$ are not zero then divide through by $x^n$ and let $z = y/x$. Can you see why equality can't hold for $z>0$? Can you see why it's false for $-2\le z<0$? (assuming $n$ is even) Can you see why it's false for $z < -2$?
Oct
20
comment Pigeon hole principle based puzzle question
The question is worded poorly: "12 pairs each of 3 different types of gloves" is $36$ pairs. "12 pairs of gloves, of 3 different types" is $12$ pairs.
Oct
20
comment Pigeon hole principle based puzzle question
"Any other scenario involves extracting less gloves, so 13 is the $minimum to be sure$." This makes it sound like there are no other scenarios where you need $13$ gloves, which isn't true. You don't need the first $12$ gloves to all have the same handedness, so I think this part deserves a little more justification.
Oct
18
comment How to prove that $\lim_{u\to \infty} (1+\frac 1u)^u = e$
@user3835165 That is not a definition. Many numbers that are not equal to $e$ match the same description. The limit in your question can't possibly be equal to all of them.
Oct
17
comment What are the odds of hitting exactly 100 rolling a fair die
Expectation by itself is not enough for the general case. Suppose $S = \{2,4,6\}$. Then the probability of hitting exactly $101$ is much lower than $2/7$ :).