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 Mar 17 comment Can a closed disc in the plane be partitioned into three disjoint sets which are pair-wise isometric? This is probably stupid, but why not cutting the cake in three equal parts (taking only half of the boundary)? Mar 9 comment Applications of the Cayley-Hamilton theorem @LSpice: well as commutator have zero trace, C-H (in dimension 2) says that $[A,B]^2$ is a scalar matrix, which therefore commutes with every other matrix $C$. One can also see this without mentionning C-H of course... Mar 4 awarded Nice Question Mar 2 comment Applications of the Cayley-Hamilton theorem One can use C-H to show some "universal" identities for matrices. For example, for every $2 \times 2$ matrices $A,B,C$, one has :$[[A,B]^2,C]=0$ (where $[,]$ is the commutator). Jan 22 comment Exact determinant of a circulant matrix This determinant is also equal to the resultant of $X^n-1$ and $P:=c0+...+c_{n-1}X^{n-1}$. This resultant can be computed efficiently by modular algorithms (as mentionned on wikipedia for example, en.wikipedia.org/wiki/Resultants#Computation). There are also so-called subresultant algorithms (variation on using Euclid algorithm to compute the resultant but avoiding to work in the rationals). Jan 5 comment Zeros of polynomials modulo non-prime @user83633 : yes of course! I was not in a good day... Dec 18 comment Zeros of polynomials modulo non-prime My previous comment is wrong: over Z/n, one root of a polynomial gives a linear factor, but two distinct roots don't give a factorization by a product of two linear factors (due to the non integrity of the ring). Dec 18 comment Zeros of polynomials modulo non-prime Since roots give factorisation of polynomials even over the ring $\mathbf Z/n$, it is equivalent to search a characterisation of subsets $S \subset \mathbf Z/n$ s. t. for every $x$ not in $S$, $\prod_{s \in S} (x-s) \neq 0$. Dec 18 comment Zeros of polynomials modulo non-prime @user83633: as the OP suggests with her example mod 6, this is not as simple (due to the condition that $p$ must be non zero outside of $S$). Dec 8 revised Concrete solution to the (oriented) Oberwolfach problem with one table added 364 characters in body Dec 8 comment Concrete solution to the (oriented) Oberwolfach problem with one table Actually, there is a concrete solution for $n=8$ on page 3 of Bermond, J.-C.; Faber, V., Decomposition of the complete directed graph into k-circuits.J. Combinatorial Theory Ser. B 21 (1976), no. 2, 146–155. But they say it was found on a computer so it does not help that much. Dec 8 comment Concrete solution to the (oriented) Oberwolfach problem with one table One reference is : Alspach, Brian; Gavlas, Heather; Šajna, Mateja; Verrall, Helen Cycle decompositions. IV. Complete directed graphs and fixed length directed cycles. J. Combin. Theory Ser. A 103 (2003), no. 1, 165–208. But then one has to remount to older and older papers, treating special cases or equivalent problems. Dec 7 comment Concrete solution to the (oriented) Oberwolfach problem with one table There is of course a non-oriented variant of the problem. I'll be glad to hear about it as well. Dec 7 revised Concrete solution to the (oriented) Oberwolfach problem with one table added 119 characters in body Dec 7 asked Concrete solution to the (oriented) Oberwolfach problem with one table Nov 19 revised When is a submanifold of $\mathbf R^n$ given by global equations? edited tags Nov 18 revised Gysin exact sequence for a singular subvariety added 7 characters in body Nov 18 revised Gysin exact sequence for a singular subvariety added 40 characters in body Nov 18 revised Gysin exact sequence for a singular subvariety edited tags Nov 17 awarded Yearling