45,323 reputation
23496
bio website www-math.univ-poitiers.fr/…
location Poitiers, France
age 54
visits member for 2 years, 9 months
seen 51 mins ago

professor of mathematics at the Université de Poitiers (France)


1h
comment Verification of binomial coefficient congruence $\binom{jp}{j}\equiv j\binom{p}{j}\pmod{p^2}$
+1. Once you've brought it down to a congruence mod$~p$, you could also use Lucas' theorem which gives: $\binom{jp-1}{j-1}\equiv\binom{j-1}0\binom{p-1}{j-1}=\binom{p-1}{j-1}$ when $j-1<p$. By the way, at the very end of your comment, you forgot to say "modulo$~p$".
3h
comment Blue Eyes: A Logic Puzzle, has a puzzling solution (a.k.a. What does common knowledge have to do with it?)
There's two different things: stating precisely what happens, as if debugging a program (which is what I tried in my answer), and proving some property of the process. For the latter, possibly after studying in detail what happens to get an idea, it is most efficient for an iterative process like the one at hand to prove by induction, even though it is not absolutely necessary for a finite process.
10h
awarded  elementary-set-theory
1d
revised Cardinality of the set of all two-element subsets of $\mathbb{N}$
added 3 characters in body
1d
revised Cardinality of the set of all two-element subsets of $\mathbb{N}$
added 837 characters in body
1d
answered Cardinality of the set of all two-element subsets of $\mathbb{N}$
1d
revised Blue eyes: a logic puzzle
added 2 characters in body
1d
comment Quadratic form in canonical form relation
Please be more clear what exactly you are asking. Canonical forms in general are distinguished representatives of certain equivalence classes; they allow to quickly see whether two elements are equivalent. Here the canonical form is a representative of the equivalence class of your homogeneous quadratic form under orthogonal changes of basis.
1d
answered Blue Eyes: A Logic Puzzle, has a puzzling solution (a.k.a. What does common knowledge have to do with it?)
2d
answered Problems that become easier in a more general form.
2d
asked Determinant of a rank-one update of a scalar matrix
2d
answered Determinant of a rank-one update of a scalar matrix
2d
answered Matrix of rank one.
2d
revised Matrix of rank one.
added 11 characters in body
2d
revised Finding the characteristic polynomial of this specific $3\times3$ matrix
more specific title
Aug
18
answered Splitting a matrix $A \in \mathbb{M}^{n \times n}(\mathbb{C})$by solving $Av = \lambda C v$ for some chosen $C$
Aug
18
answered Explain this generating function
Aug
18
comment Explain this generating function
The summation $\sum_{n=m=1}^\infty...$ is weird; if you're requiring two equal summation indices, why not just a single one instead? Did you rather mean $\sum_{n,m=1}^\infty...$ (two independent summations)?
Aug
17
revised How to solve this $2\times2$ linear system of equations?
one does not solve matrices
Aug
17
answered Relation between $\dim V$ and $\dim V^{\star}$