Apr 8 revised How to find the Galois group of a polynomial?added 1234 characters in body Apr 8 revised How to find the Galois group of a polynomial?added 958 characters in body Apr 8 revised How to find the Galois group of a polynomial?added 958 characters in body Apr 8 answered How to find the Galois group of a polynomial? Apr 8 comment Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers)I'm surprised this answer only got one vote (mine). As far as I can tell, this is the only answer which is a full proof that the answer is $495$: The minimum value of $x^2-D y^2$ is not always a convergent, if I recall correctly, but it is always found on the river. And I had not understood before reading this how easy the river is to compute. Apr 2 comment How often does it happen that the oldest person alive dies?@HaraldHanche-Olsen Looking at the data I cite above suggests that death probability is not constant with age, even among centenarians, but is growing at about $0.03$ per year. I.e. at 100, your odds of seeing your next birthday are about 75%, at 110, only 50%. That difference should matter for modeling. Apr 2 comment How often does it happen that the oldest person alive dies?Useful data here ssa.gov/oact/STATS/table4c6.html Apr 1 awarded Nice Question Apr 1 asked Would it be OK to ask people not to vote up my partial answer to a really good question? Mar 31 comment How to prove $\sum_{i=1}^{n-1}\frac{1}{\operatorname{lcm}(a_i,a_{i+1})}\lt1$ where $a_i\in\mathbb N$ and $a_i\lt a_{i+1}$?By the way, a stronger statement is true: $\sum_{i=1}^{n-1} 1/LCM(a_i, a_{i+1}) \leq 1-1/2^n$. This one is a nice challenge. Mar 29 comment When a covering map is finite and connected, there exists a loop none of whose lifts is a loop.@suissidle This doesn't make sense. Where do the endpoints of the line map to? Mar 29 comment When a covering map is finite and connected, there exists a loop none of whose lifts is a loop.You got it! Congratulations! And yes, now it is time for nontrivial group theory. Mar 29 comment When a covering map is finite and connected, there exists a loop none of whose lifts is a loop.Response to @Bartek's edit: What you have shown is that $\bigcup_{y \in p^{-1}(x_0)} p_{\ast}\left( \pi_1(\tilde{X}, y) \right) = \pi_1(X, x_0)$. This does not show $p_{\ast}(\pi_1(\tilde{X}, y))=\pi_1(X, x_0)$ for any single $y$. However, it is on the right track. For $y$ and $z$ two different preimages of $x_0$, what can you say about the relationship between $p_{\ast}(\pi_1(\tilde{X}, y))$ and $p_{\ast}(\pi_1(\tilde{X}, z))$? Mar 29 comment Is $A \times B$ the same as $A \oplus B$?@MartinBrandenburg In my experience, if $A$ and $B$ are rings, and someone writes $A \oplus B$, they mean $A \times B$. It is true that this is not a coproduct. (In the category of unital commutative rings, the coproduct is $A \otimes B$. In the category of not necessarily unital commutative rings, I believe the coproduct is $A \times B \times (A \otimes B)$. I'm not sure about the noncommutative cases.) In any case, I have never seen $\oplus$ in a category of rings used to mean coproduct, even for finite sums. Mar 29 answered When a covering map is finite and connected, there exists a loop none of whose lifts is a loop. Mar 29 comment When a covering map is finite and connected, there exists a loop none of whose lifts is a loop.Connected means that $\tilde{X}$ is connected. Have you learned the relationship between connected covering spaces and the fundamental group yet? @suissidle If $X$ is simply connected, the (corrected) hypotheses of the statement are impossible to satisfy, so the statement is vacuously true. Mar 29 comment When a covering map is finite and connected, there exists a loop none of whose lifts is a loop.Throw in "non trivial", meaning $p$ has degree $>1$, and the statement is true. It's nontrivial though even when you know what connected covering maps are, and I don't think it's reasonable to attempt without that background. Mar 29 comment Function on the unit diskSee en.wikipedia.org/wiki/Radon_transform . Short answer: yes. Mar 28 asked Why is Flattening a CoefficientArray so slow? Mar 28 awarded Nice Answer