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Okay just a few mins, finishing something.

Anyone for some casual games pretty soon?

Well done :).

Well ratings are purely a relative scale, basically a point difference maps to a statistically expected outcome. Eg the percentage of decisive games won by the higher rated player is predicted to be the same for a 2600 vs a 2500 as when a 1200 plays an 1100. The ratings stabilise toward the...

accurate in what sense? accurate in comparing skill of two lichess players or accurate to over the board ratings? for the former, they should be pretty good for comparing any two players with a decent game volume. if game count is low though it doesn't mean much either way. it's not very...

Ps. If anyone is up for some casual blitz games later tonight, I am probably down.

Am all for this. People register interest here and direct other bos users who might be interested to this thread as well. Can start with a one-off event on something like a Sunday evening, depending on numbers will either do swiss, round robin, or double elimination. (The last of these works...

Nice :). I actually forgot a term on the LHS from the diophantine equation I was trying to remember though lol, try the edited problem too. It is slightly harder, but not greatly so. The original hint still stands. Repost for visibility: Solve the equation: x^2+y^2+1=xyz over the positive...

Solve the equation x^2+y^2+1=xyz over the positive integers. Hint: First concentrate on determining what possibilities there are for z.

p-1 = mn + r for non-negative integers m, r with r < n. Then (a^r)(a^n)^m=a^(p-1) => a^r=1 (using FLT) From the minimality of n, we must conclude r=0. That is n|p-1.

Re: Extracurricular Integration Marathon a) \\ \\ I=-\int_0^{\pi/2}\frac{\cos{x}\log(\cos{x})}{\sin{x}}\, dx\\ \\ =-\int_0^1 \frac{u\log{u}}{1-u^2}\, du\\ \\ = -\int_0^1 \sum_{k\geq 0}u^{2k+1}\log{u}\, du\\ \\ = -\sum_{k\geq 0}\int_0^1 u^{2k+1}\log{u}\, du\\ \\ = \sum_{k\geq...

Re: MX2 2016 Integration Marathon Was in my office and knew my alt password off the top of my head, but would have needed to check one of those password reset emails to get my password for the main acct.

Re: MX2 2016 Integration Marathon It is perhaps a bit much to expect a current student to tackle the above integral without hints, so here is a a rough walkthrough: $1. Let $I_n=\int_{-\pi/2}^{\pi/2} \frac{\sin(2n+1)x}{x}\, dx$ and show that $I_n$ converges to the integral $I$ you are seeking...

Re: MX2 2016 Integration Marathon Note that following my own suggestion, I assumed knowledge of the sin(x)/x integral in order to compute the above. So treating it as a separate question, prove that: \lim_{R\rightarrow\infty}\int_{-R}^R\frac{\sin(x)}{x}\, dx=\pi I will give students a...

Re: MX2 2016 Integration Marathon Okay, I think it's been long enough so I will post my solution. If you feel you are making progress then keep trying yourself before reading the below!! For starters, let's assume a and b are positive, as changing the sign of one of these guys literally...

Re: MX2 2016 Integration Marathon By all means, I think it's fairly fun :). Will post my solution later if it remains unsolved here.

Re: MX2 2016 Integration Marathon Okay, would people like me to post a solution to my old one then? Or is anyone still trying it?

Re: HSC 2016 4U Marathon Am well aware of how to estimate the error in Newton's myself lol, am posing this as a question to HS students. Don't have a copy of that book on me so I cannot speak for how rigorous the method in that question is. Even if it does things properly though, I highly...

Re: HSC 2016 4U Marathon Good first idea! Newton's is indeed amazing for this purpose. However, your analysis of accuracy is a bit flawed. The n+1-th approximation being very close to the n-th approximation doesn't in itself imply that we are close to the limiting value. Picture a sequence...

Re: HSC 2016 4U Marathon Sure, but "fast" is relative. It is not immediately clear whether the time taken to exponentiate and take the logarithm of a quantity will be short enough to offset the time saved by translating an "n-th root problem" to a trivial one-step "division by n problem". The...