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Apr
10
comment What's problematic about finding out if a large number is Prime or not?
@Bakuriu: Concerning your 1st sentence: In my present humble understanding, each additional run of Miller-Rabin reduces the probability that a composite number yet fails to be revealed by the test by a certain finite factor. If that's indeed the case, then there could theoretically exist cases that even with an arbitrarily large number of trials of Miller-Rabin such defects could occur. Do you happen to have references proving the sufficiency of a certain upper bound of trials of Miller-Rabin?
Apr
10
comment What is the idea behind Green's function? What does it do?
You are not rude at all. I am not a mathematician but engineer and hence the part of math that I learnt is likely to be fairly biased to practical uses. Anyway, my lecturer recommended to try Green's function when one encounters non-homogeneous BVP (so yes, sort of cooking receipt).
Apr
10
comment What's problematic about finding out if a large number is Prime or not?
However, for practically interesting cases of large numbers (e.g. of the order of those employed as moduli for RSA encryption), AKS is nonetheless not a practically favourable method, for it would take too much computing time, despite some later improvements of it, if I don't err. One commonly employs the probabilistic method of Miller-Rabin, which doesn't prove the primality, in case it fails to find that the number is composite. (I read somewhere a suggestion to additionally do the Lucas test.)
Apr
10
comment What is the idea behind Green's function? What does it do?
Wiki says: "The primary use of Green's functions in mathematics is to solve non-homogeneous boundary value problems." Doesn't that somehow satisfies your need?
Apr
10
comment Intuitive explanation of entropy?
I just want to point out that there are simple pieces of software around on the Internet claiming to determine (and in fact they do correctly compute according to the formula of Shannon) the "entropy" of a user-given character sequence. However, entropy is a concept relevant to the source of randomness, not to a particular "given" sequence. Hence such calculations are problematical. See the thread crypto.stackexchange.com/questions/33231/entropy-calculation
Jan
19
comment prove that $ \binom{n-1}{0} +\binom{n}{1}+\binom{n+1}{2}+\cdots+\binom{n+k}{k+1}=\binom{n+k+1}{k+1}$
When you apply your identiy to RHS and simplify, you obtain the same problem but one step smaller. So you could continue to do the reduction.
Sep
24
awarded  Yearling
Dec
20
awarded  Constituent
Dec
16
awarded  Caucus
Sep
24
awarded  Yearling
Aug
24
revised Special solutions to Ax = 0
added 62 characters in body
Aug
24
answered Special solutions to Ax = 0
Aug
20
comment Special solutions to Ax = 0
Given an arbitrary mn matrix M, how should one algorithmically go about to compute its null space (that contains all vectors v with Mv=0)? Thanks in advance.
Apr
28
asked Probabilities of throws of Archimedian solids
Mar
28
answered Matrix with determinant 0
Mar
27
awarded  Supporter
Mar
23
awarded  Tumbleweed
Mar
10
comment What exactly do eigenvalue and eigenvector indicate?
See mathworld.wolfram.com/Eigenvalue.html which has a sentence about that.
Jan
26
comment proving that a point is the center of a circle
There seems to be an error in the formulation of the problem. For if that's generally true, then it is impossible to have 10 (a constant) in DE = 10 + AB.
Dec
25
comment The last three digits of $3\times7\times11\times15\times \cdots \times 2003$
Sorry, typo: Please read: "we have f(500)=875".