Tag Archives: open problem

The danger of confusing cosets and numbers

As I mentioned yesterday, I’d like to consider a proposed proof of the Goldbach Conjecture that has garnered some attention, at least some attention from people who ask me about things like the validity of proofs of the Goldbach Conjecture. I like this in particular because it illustrates how I look through some papers (those towards which I’m a bit skeptical) and it illustrates a problem I’ve seen before: switching between interpreting a number as an element of the integers and an element of $latex \mathbb{Z}/n\mathbb{Z}$. (There is a certain problem with this, in that although I ‘do number theory,’ were the conjecture proved it is almost certain that I would be not at all familiar with the methods of proof).
In particular, I’ll be looking at the 19 August 2012 preprint “The Goldbach’s conjecture proved” by Agostino Prastaro (the pdf is here). The rest after the fold –

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Containers of Water II

In a previous post, I considered the following two questions:

Questions
What sets $latex S $ maximize $latex |{\bf F}(S;p)| $ for various $latex p$?
What sets $latex S $ maximize $latex \lfloor {\bf F}(S; p) \rfloor $ for various $latex p$?

I then changed the first question, which I think is perhaps not so interesting, to the following:

What sets S maximize |{\bf F}(S;p)|_c, where |\cdot|_c denotes the largest connected interval of results?

Let’s explore a few cases to see what these answers might look like.

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Posted in Math.REC, Mathematics, Open | Tagged , , | 1 Comment