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Jul
16
answered If $G$ is a group with order $99$, it is cyclic by Sylow (isn't it?). I want to find a generator.
Jul
16
comment A congruence equation
Chinese remainder is clearly not usable, $13$ is prime. Do you even know what CRT says?
Jul
16
comment Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?
$67$ also works.
Jul
16
answered A congruence equation
Jul
16
comment Unions of subspaces
"However, $w_{ij} \not \in W_j$ for all $j \neq i$" I don't think this is true.
Jul
16
answered Unions of subspaces
Jul
16
answered How many $5$ element sets can be made?
Jul
16
answered Inverse of elements in a group
Jul
16
accepted A positive integer is equal to the sum of digits of a multiple of itself.
Jul
16
comment Fast way to get a position of combination (without repetitions)
How efficient does it need to be with respect to the length of the $k$-tuples? can it be cuadratic over $k$?
Jul
16
comment Place maximum Rooks on a chessboard
Well, if you have one hole in one of the corners and the other hole near the center of the board the answer will be $9$.
Jul
16
revised Place maximum Rooks on a chessboard
deleted 2 characters in body
Jul
16
comment Place maximum Rooks on a chessboard
+1 for tedious but doable.
Jul
16
comment Place maximum Rooks on a chessboard
Yes, that is correct. Henning Makholm is making a description of when the max is $8$, when it is $9$ and when it is $10$.
Jul
16
answered Place maximum Rooks on a chessboard
Jul
16
comment Place maximum Rooks on a chessboard
$10$ is possible, if the holes are well placed. Let me make a drawing.
Jul
16
comment Place maximum Rooks on a chessboard
For example, if the holes are in corners then clearly the answer is still $8$.
Jul
16
comment Place maximum Rooks on a chessboard
I think answer is $10$ if the coordinates of the holes are sufficiently far apart and the holes are not on the edge. And less depending on the position.
Jul
16
comment Can $x\pi$ be rational?
if $x$ is algabraic and irrational (hence non-zero) then $\pi x$ is going to be trascendental so the answer would be $b$.
Jul
16
accepted What is the intuition behind generating functions? What makes them valuable?