awllower

it is late here and I shall sleep now. Good night. :)

You may see the answer and point out any inappropriate points. :)

Briefly, because $$a_{n+1}=d_1+\cdots+d_{n+4}+d_{n+5}=a_n+a_n=2a_n.$$

I am writing an answer; I shall add an explanation.

It should be $a_3=2a_2=4\cdot28.$

basically $a_{n+1}=2a_n.$

glad to know that. :D

how about $28=1+2+4+7+14?$

yes, I mis-typed.

that is, $d_{n+5}=d_1+\cdots+d_{n+4}.$

I mean $a_{n+1}=2(d_1+\cdots+d_{n+4})$

hi

How about $d_{n+5}=d_1+\cdots+d_{n+4}?$

In your construction how are you sure that $d_1$ divides $a_{n+1}?$

Alright, so it remains to find one such $a_1?$ Also isn't $a_{n+1}$ supposed to be $\sum_{r=1}^{n+5} d_r?$

Does anyone want to add some more proofs to this question, just for fun? :P

Does anyone know why Makoto Kato has been suspended?

BTW, that problem turns out to have an answer here

Same here. :)

Quite a difficult group-theoretical problem

:D

Who said what?

XD

The length is indeed a pain.

:"D

Hello everyone!

Because their differrence is infinitely small?

Strange question

Je suis d'accord~

Oh, et j'ajoute quelques mots de plus. Peut-être il y a de nouvelles erreurs. ;)

Et merci pour tout!

@Laure J'ai édité mon profil en conséquence.

the equivalence in George's answer is a generalisation of what I am trying to prove; so I cannot take that as granted.

Sorry for the impolite tone; I was too excited to find this statement.

...for I...

I shall ponder more upon it, or I suspect something is wrong, but I don't know where.

I mean this is the definition.

This is exactly how a professor told me. :)

I think here the morphism u is a morphism of sheaves; and I am not familiar with the notion of projective sheaf of modules. Maybe you can explain more? Thanks.

I am currently trying to read EGA; and I was confronted with a proposition that, hypotheses being as in the question, an $\mathscr O_X$-module is coherent if and only if it is $\cong \tilde M$ where $M$ is a finitely generated $A$-module. I cannot uderstand the last step of that proof, but I can complete it if I can show the statement in question. Also, it is mentioned that $\mathscr O_X$ is not necessarily a coherent $\mathscr O_X$-module.

I cannot understand the proof: Say I have a morphism $u:\mathscr O_X^n|_U\rightarrow \mathscr O_X|_U;$ how did you propose to prove that $\operatorname{Ker}(u)$ is locally finitely generated?

I don't understand what you are trying to prove here: are you trying to show that $\mathscr O_X$ is always a coherent $\mathscr O_X$-module? I think this is not true in general.

I see. Thanks for explaining.

Hello!