Erick Wong
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 5h comment Derive an inequality using Summation by Parts Also, do you mean $x = \pi/m$? Of course it's arithmetically equivalent to $m = \pi/x$, but the latter is a very confusing way to describe this relation since $m$ has to be an integer but $x$ would otherwise be an unconstrained real parameter. 5h comment Derive an inequality using Summation by Parts You really need to say more about $a_n$. The left side depends on the relative sizes of $a_{m+1}, a_{m+2}, \ldots, a_{n+p}$. There's no way the right hand side can bound that when it only depends on the first coefficient. 6h revised Multiplication of two successive Fibonacci numbers added 11 characters in body 6h comment Solve equation $\frac{1}{x}+\frac{1}{y}=\frac{2}{101}$ in naturals It's not at all clear how this helps determine all solutions. 6h comment Why does Ln x start higher on the graph than log x? They follow eacthother but Ln is always higher. It doesn't start higher, actually. When $x$ is between 0 and 1, then $\ln x$ is actually lower than $\log x$. 7h comment Showing that Harmonic numbers are $\Theta(\log n)$, intuitively @Nakano $H_n$ is precisely the integral of the stepwise-constant function depicted in vonbrand's answer. Call this function $f(x)$. Now note that $f(x) \ge 1/x$ and integrate. To get an upper bound use a similar idea but you might need to pull off the first term to avoid the singularity at $0$. 7h comment Showing that Harmonic numbers are $\Theta(\log n)$, intuitively I don't understand how it's not a proof. It's a straightforward application of the fact that if $f(x) \ge g(x)$ on some interval $[a,b]$ then $\int_a^b f(x) dx \ge \int_a^b g(x) dx$. There are details that need to be filled in but you asked whether it was valid, not whether it was fully worked out in detail. 7h answered Showing that Harmonic numbers are $\Theta(\log n)$, intuitively 7h comment Showing that Harmonic numbers are $\Theta(\log n)$, intuitively Of course the integral comparison is valid, once you fill in the details. Did you have a look at vonbrand's answer in the post you linked to? math.stackexchange.com/a/306674/30402 7h comment Is $k+p$ prime infinitely many times? The distinction between "prime gap" and "primes with difference $k$" is immaterial in this "$\le 246$" formulation. In fact I believe the sieve methods used here just establish "there are infinitely many blocks of width 246 containing at least two primes". The equivalence to "some prime gap $\le 246$" is easy. 1d comment Given $k$, are there infinitely many $n$ so that $w(n) = w(n+k)$? @user336-iactuallychosethis Maybe you could post a new question which describes the amount of detail you're looking for specifically? 2d revised Prove that $\frac{7}{12}<\ln 2<\frac{5}{6}$ using real analysis edited body 2d comment Prove that $\frac{7}{12}<\ln 2<\frac{5}{6}$ using real analysis @JaumeOliverLafont Yes, corrected. Thanks! 2d answered Prove that $\frac{7}{12}<\ln 2<\frac{5}{6}$ using real analysis 2d answered Given $k$, are there infinitely many $n$ so that $w(n) = w(n+k)$? 2d comment Given $k$, are there infinitely many $n$ so that $w(n) = w(n+k)$? Actually I found a 2011 citation that builds on the prior result to prove this for $k=1$ (if so, then likely it extends to other values of $k$ as well). Will post the details later. 2d comment Given $k$, are there infinitely many $n$ so that $w(n) = w(n+k)$? Goldston, Graham, Pintz and Yildirim have shown that for at least one of $k=2,4,6$ the equation $\omega(n)=\omega(n+k)=2$ holds infinitely often. This is a much stronger equality but not as universal in $k$. Feb 9 comment Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square @zhoraster Or in a similar vein to (but slightly different from) the Euler brick problem, take any 3-partition of $\mathbb N$ and take $f(x)$ to be constant on each partition with one of the values $15842$, $72962$, $216482$. Probably this won't scale easily to 4 values... :) Feb 8 revised Different Ids on mars retagged Feb 5 comment About the proof of the four colour theorem @user1952009 There has been a lot of progress in automated proof checking over the last few decades. Various amounts of human input are used in transcribing the statement and proof of a theorem, but once accomplished there is only a small amount of base logic that one needs to trust/verify (and that the encoding of the theorem matches what we associate to the name). Many people feel that automatic verification adds much more certainty to the validity of a proof.