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11347
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location Monkey Island, OK
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visits member for 2 years
seen 6 hours ago

16h
comment Why do probabilists have a preoccupation with urns?
Because urns are smooth and round objects, it is simple to create a model for how the balls roll inside them.
17h
comment What is difference between Fourier Transform and Fast Fourier Transform?
the difference is the speed.
1d
comment Perfect matching for graph with exactly $k$ edges for every node
Hall's marriage tells you there is a saturating mathcing of $A$, but since |A|=|B| this must mean this is a perfect mathcing.
1d
comment Combinations with replacement
I don't doubt the answer is correct, but by the comment on my answer from the op I think what the meant is that the committee doesn't necesserily have to be of five persons, moreover for each task there is exactly one person with that task.
1d
comment Combinations with replacement
I don't see why someone would downvote this answer, the question was unclear.
1d
comment Combinations with replacement
Oh, I think I understand now. I will edit.
1d
comment time and distance
Oh, they are right, because at minute 26 they are both at the edge, but at different edges, so they never shake hands at the edge. That means the answer is indeed 19.
1d
comment Why is mathematics not reducible to logic?
what do you mean?
2d
comment How to compute the coefficient of an equation?
the multinomial theorem allows you to compute the external coefficient, you then need to calculate what the internal coefficient of each of the powers will be and multiply the external coefficient with all the internal coefficients, this will give you the result. Notice in this example the external coefficient was 210, and all the external coefficients were 1 except for the coefficient for the $y^2$ term, which was $4$.
Jul
7
comment Graph with edge disjoint cycles
I think you mean it has at least $\lfloor \frac{n}{2} \rfloor$ disjoint cycles since for example: a $K_4$ doesn't have at least 1.5 disjoint cycles.
Jul
6
comment How find the greatest odd number $N$, such for any odd $k(<N)$ if $(N,k)=1$,then $k$ is prime number.
Yeah, that's where Bertrand comes in
Jul
6
comment How find the greatest odd number $N$, such for any odd $k(<N)$ if $(N,k)=1$,then $k$ is prime number.
I made a typo, it should be 105=3*5*7
Jul
6
comment The only fixed-point free automorphism of order $2$ is $\phi(a)=a^{-1}$(in a finite group)
Yes, I'm pretty confident on the last part, it was the earlier part I wasn't completely sure on. Thank you Hagen.
Jul
6
comment How find the greatest odd number $N$, such for any odd $k(<N)$ if $(N,k)=1$,then $k$ is prime number.
base case: $3*5*7*11>13^2$. We now use induction, where the inductive hypothesis is $3*5*7*11* \dots p_k>p_{k+1}^2$. Clearly $p_k+1>4$ so $3*5*7*11\dots *p_k*p_{k+1}>43*5*7*11* \dots p_k>4(p_{k+1}^2)\geq 4p_k$.The last inequality comes fro bertrand's postulate.
Jul
6
comment How find the greatest odd number $N$, such for any odd $k(<N)$ if $(N,k)=1$,then $k$ is prime number.
because if we had $a>(p_k)^2$ then that number would be comprime to $a$, smaller than $a$ and not a prime, which is exactly what you don't want. Moreover if that number is larger than $a$ then so are all of the other odd numbers coprime to $a$ and which are not perfect squares.
Jul
3
comment How do I define a string in formal language by means of a definition of tuple?
@novice, I don't know, I'm merely giving my opinion, take a chill pill.
Jul
3
comment How do I define a string in formal language by means of a definition of tuple?
can't you do the same thing? $(a,b,c)=\{a,\{a,b\},\{a,b,c\}$
Jul
3
comment Is this procedure for $5^{300} \bmod 11$ correct?
you didn't explain anything, why are you adding all those numbers?
Jul
3
comment Zombie outbreak on a $k$-regular graph
+1 for zombies!
Jul
2
comment Is a finite group with a certain automorphism must be abelian
I didn't know this, could you provide a link to that please? I can't find it in the wikipedia article you provided.