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2h
comment On power residues
Ok, still, how about $n=2$?
2h
comment On power residues
Could you prove this for $n=2$? Is it true that if $m$ is large enough, then there are at least two (distinct) elements $b\in{\mathbb Z}_m$ such that both $b$ and $b^2$ belong to $(\sqrt m,\sqrt m\log m)\pmod m$? Have you tried using exponential sums to prove this?
Feb
7
comment Does $|A+A|$ concentrate near its mean?
You have $|A+A|=I_0+I_1+\dotsb+I_N$, where $I_z$ is the indicator random variable of the event $z\in A+A$. It may be a little technical, but should not be difficult in principle to show that the $I_z$ are "almost independent", the exact meaning of which is that the pair correlations of $I_u$ and $I_v$ are small for $u\ne v$. As a result, $|A+A|$ should have a distribution close to the binomial.
Feb
7
revised Does $|A+A|$ concentrate near its mean?
edited tags
Feb
4
comment If $N = qn^2$ is an odd perfect number, is it possible to have $q + 1 = \sigma(n)$?
What is an "Euler prime"? What is a "quasi-Euler prime"? What is $I(n)$?
Jan
23
comment Question related to Fermat curve: Does the equation $A x^n + By^n = C z^n$ have any solution in $\mathbb{N}$?
... or $z=1$ and $C=Ax^n+By^n$ ...
Jan
19
awarded  Nice Question
Jan
17
comment Sharpening the Loomis-Whitney inequality
@Fedor Petrov: you are right; I was sure that BT is strictly stronger than LW and have not checked carefully. I "simplified" my question following your remark.
Jan
17
revised Sharpening the Loomis-Whitney inequality
deleted 262 characters in body; edited title
Jan
17
comment Sharpening the Loomis-Whitney inequality
@Fedor Petrov: how would you derive BT from LW?
Jan
17
asked Sharpening the Loomis-Whitney inequality
Jan
9
comment monotonicity of a function
What is squared in the numerator: ${\rm sinh}$ or its argument only? What is the motivation behind this question? (Sounds like a homework problem to me, and asking homework questions is strongly discouraged at this site.)
Jan
2
revised Kruskal-Katona for multisets?
(some?) typos fixed
Jan
2
asked Kruskal-Katona for multisets?
Dec
21
comment Maximal size of minimal generating set
What if $G$ is not abelian of square-free exponent? As I understand if, the PO wants to know $D(G)$ precisely for all finite groups $G$.
Dec
21
revised Maximal size of minimal generating set
deleted 54 characters in body
Dec
18
comment Difficulty understanding equivalent statement of Erdős Discrepancy Problem
Assuming that the second statement is wrong, fix $C>0$ such that for each $N>0$, there is a sequence $(f_1,\dotsc,f_N)$ with $\left|\sum_{j=1}^n f_{jd}\right|\le C $ whenever $nd\le N$. Since there are only two possible values of $f_1$, among these finite sequences there are infinitely many sharing the same value of $f_1$. Among them, there are infinitely many sharing the same value of $f_2$, etc. Acting in this way, you construct an infinite sequence $(f_1,f_2,\ldots)$ which inherits the small discrepancy property from the finite sequences used o construct it.
Dec
12
revised Freiman-isomorphic sets
added 1590 characters in body
Dec
11
comment Kruskal-Katona for homocyclic groups?
Let us continue this discussion in chat.
Dec
10
comment Kruskal-Katona for homocyclic groups?
@FedorPetrov: yes. This was somewhat implicit in my question, I made it more explicit now.