Is my evidence correct?

Wetzlar, Germany, pensioner, e-mail: Mykhaylo Khusid Representation of even number in the form of the sum of four simple.
Abstract: Harald Andres Helfgott finally solved 2013 a weak problem of Goldbach.


where at the left the sum of three prime numbers, on the right odd numbers, since 7 The author provides the proof in this work, being guided by the decision

weak problem of Goldbach that: p1 + p2 + p3 + p4 = 2N [2] where on the right sum of four prime numbers, at the left any even number,

since 12, by method of mathematical induction. Keywords: On this basis, solves two actual problems of the theory numbers Decision.

  1. For the first even number 12 = 3+3+3+3.

We allow justice for the previous N> 5: p1 + p2 + p3 + p4 =2N [3] We will add to both parts on 1 p1 + p2 + p3 + p4 +1 =2N +1 [4] where on the right the odd number also agrees [1] p1 + p2 + p3 + p4 +1= p5 + p6 + p7 [5] Having added to both parts still on 1

     p1 + p2 + p3 + p4 + 2= p5 + p6 + p7 +1               [6]          We will unite    p6 + p7 +1    again we have some odd number, 

which according to [1] we replace with the sum of three simple and as a result we receive: p1 + p2 + p3 + p4 + 2= p5 + p6 + p7 + p8 [7] at the left the following even number is relative [3], and on the right the sum

four prime numbers. p1 + p2 + p3 + p4 = 2N [8]

Thus obvious performance of an inductive mathematical method. As was to be shown.

2.Any even number starting with six is representable in the form of the sum of two

prime numbers. Goldbach-Euler’s hypothesis.

We will break [8] for two sums: p1 + p2 =2K [9] p3+ p4 =2K1 [10] [10] – possible even number. .

Let there is an even number which isn’t representable in the form of the sum of two the simple 2K2 . Then exists [8]: 2N2 = 2K2 +2K1 [11] 2K2 = 2K =p1 + p2 [12] that completely contradicts the assumption of existence of the even

numbers of two simple which aren’t provided in the form of the sum. They do not exist! 3.Thus we proved: Any even number since 6 is representable in the form of a bag of two odd

the simple. p1 + p2 =2N [13]

Any even number is representable in the form of the sum of two simple. In total

even numbers, without exception, since 6 are the sum of two prime numbers.

Goldbakha-Euler’s problem is true and proved! 4. On the basis above the proved we solve one more fundamental

task. 5. Any even number, since 14, is representable in the form of the sum of four

odd prime numbers, from which two twins. p1 + p2 + p3 + p4 = 2 N [14] Let p3, p4. . – prime numbers twins, then a difference of any even,

since 14, and the sums of twins too even number which agrees,

the proved Goldbach-Euler’s hypothesis it is equal to the sum of two simple. Further we will arrange prime numbers from left to right in decreasing order.

6.And in case even number, 2 N =2 p2 +2 p4 + 4 then p1 , p2 .

inevitably also twins. We will subtract [14] sum from both parts 2 p2 +2 p4 : p1− p2 + p3 − p4 = 4 [15] From [15], obviously, p1 , p2 . – inevitably twins. 7. Prime numbers of twins infinite set. Let their final number and last prime numbers twins p3, p4. . We will designate two prime large numbers than p3, p4. . as p1 , p2 . .

We will summarize all four prime numbers and then according to item punkt6 there is even number 2 N, at which inevitably big p1 , p2 . twins. And further substituting in the sum instead p3, p4. . of numerical values p1 , p2 . process becomes infinite.

Literature: 1. Wikipedia.

Understanding when assumptions are sufficient for induction proofs to be logically correct.

Assuming that we know $ P(0)$ and $ P(1)$ and $ (\forall n \in N) \space P(2n)\Rightarrow P(2n+2)$ is it sufficient to prove $ \forall n P(n)$ ?

Intuitively I think the answer is no, but I can’t find a valid argument to “convince myself”. I think we would not be able to prove $ P(3)$ correct?

Which is the correct subset of a given number with conditions?

1) the sum of the proper divisors (including 1 but not itself) of the number is greater than the number itself

2) no subset of those divisors sums to the number itself.

For example:

  • Number 12: the proper divisors are 1, 2, 3, 4 and 6. The sum is 1+2+3+4+6 = 16 which is greater than 12 and matches the first condition. However, the subset 2+4+6=12 which violates the second condition.
  • The correct answer for the problem above is 1,3,4,6 because the sum of them is greater than 12 and none of the subsets equals with it.

NOTE: I have tried to solve it, but I don’t understand the approach of the problem. I can get the divisors of the given number and I can check if the sum of them is greater than the given number.

My problem is, I don’t know how can I get all of the subsets and decide which of them meet the requirements of the 2 listed contitions.

Are the following Mathematica codes correct for solving wave equation PDE?

I wanna solve the following PDE of wave equation using Mathematica.

$ u_{tt}=u_{xx}$

$ 0<x<\pi , t>0$

Initial Conditions:

$ \begin{cases}u(x,0)=sin(x) \u_{t}(x,0)=1\end{cases}$

Boundary Conditions:

$ \begin{cases}u(0,t)+u_{x}(0,t)=1\u(\pi,t)+u_{x}(\pi,t)=-1\end{cases}$

  • I know the boundary and initial conditions are inconsistent.

Are the following codes correct?

weqn = D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}]; ic = {u[x, 0] == Sin[x],Derivative[0, 1][u][x, 0] == 1 }; bc = {u[0, t] + Derivative[1, 0][u][0, t] == 1,     u[Pi, t] + Derivative[1, 0][u][Pi, t] == -1}; sol = NDSolve[{weqn, ic, bc}, u, {x, 0, Pi}, {t, 0, 10}]; 

Cannot get subscriptions to send out at correct intervals

I set up the “subscriptions” module and have set it so that all members of the page have access to a number of panels. One allows them to set the frequency of emails, one allows them to pick and choose which nodes to subscribe to. The node choice works well, and so does choosing a ‘digest’ choice for the emails.

The issue I am having is that the notification emails are sent out at what seems to be the first cron event after the new content has been added, which can be a long time if I don’t visit the site, but at the same time too soon if someone has chosen a longer interval.

I am currently the only one ‘testing’ the site so have two users set up with subscriptions. One I have set for once every 3 hours and one ‘once per day’.

As Cron was only running when either entering the site or running manually, I also chose to download the module “Ultimate Cron” which I thought would run Cron more often (i have it set to 30 minutes), but it does not seem to be doing this either, although messages are being sent to both users, even if the one asking for a message no more than once per day has already received one in that 24 hour period.

If I don’t visit the site, both now get messages at least, but not at the correct intervals.

One of the main organisers of our organisation says she will not join the forum and member site unless there is a way to get notifications once a day, or once a week, and she is trying to push to use Yahoo forums, but I have everything set up the way I like it and so if I can fix this one issue I can then open it up to members of our small society.


If you need any particular screenshots of settings etc. then please let me know. I am unsure what to share at this point.

How to correct a passport stamp in the UK?

My daughter is visiting the UK from the US for a semester study-abroad program. Because it is less than 6 months, she doesn’t need a Tier 4 visa. She arrived a few weeks before the program started in order to do some sight-seeing, staying with friends. She didn’t notice right away, but the IO stamped her passport with a visitor stamp, rather than a short-term study stamp, even though she gave him the letter from the school. The school requires her to have the short-term study stamp. They have recommended that she either try to speak to an IO at Heathrow to get the correct stamp, or leave an re-enter the country.

If she were to visit Heathrow, how would she go about trying to contact an IO, given that they are stationed at the arrivals gate. Or, is there another way to go about this that doesn’t involve leaving the country?

Littlewood’s three precepts of refereeing in mathematics: is it (1) new, (2) correct, (3) interesting?

I have a question regarding Littlewood’s three precepts of refereeing a mathematical paper, namely whether it is (1) new, (2) correct, and (3) interesting.

I have found these mentioned in the literature on refereeing, e.g.:

  • “you should address Littlewoods’s three precepts: (1) Is it new? (2) Is it correct? Is it surprising?” (Krantz, 1997, p. 125); or
  • “the fundamental precepts ‘Is it true?’, ‘Is it new?’, and ‘Is it interesting?’ to which, Littlewood believed, a referee should always respond.” (Moslehian, 2010: 1245)

Unfortunately, I haven’t been able to track down the original source. Does anyone know where Littlewood might have formulated these three precepts?

Thank you!


Krantz, S. G. (1997). A Primer of Mathematical Writing: Being a Disquisition on Having Your Ideas Recorded, Typeset, Published, Read, and Appreciated. Providence, RI: American Mathematical Society.

Moslehian, M. S. (2010). Attributes of an ideal referee. Notices of the American Mathematical Society, 57 (10), 1245.

Then $A $ is choose the correct option

let $ A$ be the set of all invertible upper triangular matrics in $ \mathbb{M}_n (\mathbb{R})$ where $ n \ge 2$

then $ A $ is

choose the correct option

$ 1.$ dense

$ 2.$ Nowheredense

$ 3.$ open

$ 4.$ closed

My attempt :I take $ A = \begin{bmatrix} 1& n \0&-1 \end{bmatrix}$

I know that set of all invertible matrix is dense. You know that my given matrix $ A$ in invertible and upper triangular, so $ A$ must be open and dense

Therefore the correct option is option $ 1)$ and option $ 3)$

is its true ?

Any hints/solution will be appreciated

thanks u

Is it correct to say the field of complex numbers is contained in the field of quaternions?

I believe it is correct to refer to the complex numbers and their ‘native algebra’ a field. See for example Linear Algebra and Matrix Theory, by Evar Nering. I assume the same may be said for the set of Quaternions. Please correct me if that is wrong.

Based on that assumption, I ask: is the field of complex numbers are a subset (sub-field?) of the quaternions in the same sense that the real numbers are ‘contained’ in the complex numbers?

Is there a term for such a subordination of number fields?

I admit that I am reaching well beyond my realm of familiarity, and that my question may be nonsensical to those who are more knowledgeable in these matters.