Micah
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 Aug 8 revised Integer solutions using PIE typos Aug 8 comment Proof of the Binomial theorem; does ${n-1}\choose{n}$ make sense? If you're going to use a definition of binomial coefficients that works for arbitrary $k$, it seems like you might as well state the binomial theorem as $(x+y)^n=\sum_{k \in \Bbb{Z}} \binom{n}{k} x^ky^{n-k}$ and avoid having to do anything at all at the boundary... Aug 8 comment Proof of the Binomial theorem; does ${n-1}\choose{n}$ make sense? To your list of possible definitions, you might add: recursively, via Pascal's identity $\binom{n+1}{m}=\binom{n}{m} + \binom{n}{m-1}$. It's certainly possible in that case to avoid defining $\binom{n}{m}$ for $m \not\in \{0,1,\dots n\}$ if you choose your boundary conditions correctly, but it's a lot more straightforward to just define $\binom{0}{m}$ for all $n$ and be done with it... Aug 8 comment Primes of the form .$..55555444433322122333444455555…$ If there is, $n$ must be of the form $3k+1$ (or your number will be a multiple of $3$). Aug 8 reviewed Reopen Show that a graph has a unique MST if all edges have distinct weights Aug 5 comment What is the reason behind the current Order of Operations? (PEMDAS) You can write polynomials without parentheses if you use the other order — they just wind up being written in terms of their roots instead of their coefficients. I think in order for this answer to be complete you need to present an argument for why "polynomials written in terms of their coefficients" is a more natural concept than "polynomials written in terms of their roots", not just why polynomials are a natural concept in general... Aug 5 comment What is the reason behind the current Order of Operations? (PEMDAS) Aug 4 awarded Copy Editor Aug 4 awarded Autobiographer Aug 4 revised Wilson's Theorem - Why only for primes? deleted 141 characters in body Aug 4 reviewed Reopen Wilson's Theorem - Why only for primes? Aug 4 revised Finding all the triangles $ABC$ satisfying $\sum \frac{a^{2}\cos\frac{B-C}{2}}{\sin\frac{A}{2}}=2(a^2+b^2+c^2)$ \dfrac in titles takes up too much vertical space (especially when nested) Aug 2 revised Finding the Zeroes of a Second Derivative to Determine Points of Inflection http://www.angryflower.com/247.html Aug 1 revised How can I obtain this division's limit without using derivatives? edited title Jul 31 comment Is it possible to solve sudoku without backtracking? You may be interested in playing with this solver. It's worth noting that 1) it has an extensive list of deductions it can use, including some that are too non-local to fit in the paradigm of "Eliminate the digits which are not suitable for that cell by looking in the row, column and the smaller square to which the cell belongs", and 2) there are still some grids it can't solve (including the last few in the example popup). Jul 30 reviewed Looks OK In statistics using a regression analysis in SPSS - - variables are hunger and amount of dancing Jul 30 reviewed Leave Open About the integral $\int_{-1}^1 \frac{1}{\pi^2+(2 \operatorname{arctanh}(x))^2} \, dx=\frac{1}{6}$ Jul 30 reviewed Leave Open Line Integral: $\int_C{x^2}\:dy$ Jul 29 revised Show that if $T_1$, $T_2$ are normal operators that commute then $T_1+T_2$ and $T_1T_2$ are normal. deleted 1 character in body; edited title Jul 29 reviewed Looks OK How to solve a bi-quadratic equation with symbolic coefficients?