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Nov
22
comment Number theory and physics
But why is that a relation to number theory? E.g. the constant $\sqrt{6\zeta(2)}$ appears everywhere.
Nov
22
reviewed Close What is a zero-mean error?
Nov
22
reviewed Close Collecting sufficient conditions for Sorli's conjecture on odd perfect numbers
Nov
21
comment A remarkable sum over partitions
If you multiply both sides by $n!$ the LHS is the total number of permutations in $S_n$ and the RHS counts those with a given cycle structure $k_1$ cycles of length $a_1$, etc.
Nov
18
comment Primes $P_{2n-1}$ that are $2$ mod $3$
@DouglasZare: Ok, that makes sense! And yes, I like your edit!
Nov
18
comment Primes $P_{2n-1}$ that are $2$ mod $3$
Any particular reason for the downvotes?
Nov
17
awarded  Necromancer
Nov
17
awarded  co.combinatorics
Nov
16
answered Factorials in Pascals Triangle
Nov
16
comment How to get a good upper bound on $\sum_{1 \lt d, d|n} \phi(d)/\log d$?
The $\ll n \log n$ step is not correct. You can bound it by $n 2^{\omega(n)}$, but this may not be bounded by $n\log n$ since $2^{\omega(n)}$ can be as large as $2^{\log n/\log \log n}$. Of course the spirit of your proof is fine!
Nov
16
comment The number of integral solutions to $x^2+y^2-az^2=0$
The answer below gives a nice reference. But this particular case is pretty easy. Clearly one can assume that $a$ is an integer and a sum of two squares. Then you are asking for $\sum_{z \le T} r(az^2)$ where $r(n)$ is the number of ways of writing $n$ as a sum of two squares. This is essentially summing a multiplicative function, which is $3$ on primes $p$ that are $1\pmod 4$ (and not dividing $a$), and $1$ on the primes $p$ that are $3\pmod 4$. The usual argument via Dirichlet series now gives the asymptotic.
Nov
15
reviewed Leave Closed Can one expect the existence of a relevant approach for a proof of the Riemann hypothesis using Mochizuki's theory?
Nov
15
comment How many random sieve operations to decimate the set {2,…,n}?
That's very nice. A standard argument (Selberg-Delange) will show that $\sum_{k=2}^{n} 1/d(k)$ is about $Cn/\sqrt{\log n}$ for a constant $C$. And your sum is asymptotically the same up to error terms that are smaller.
Nov
15
comment Can one expect the existence of a relevant approach for a proof of the Riemann hypothesis using Mochizuki's theory?
I'm sorry but this is a terrible question. What is the point of speculating on how Mochizuki's work (which no one seems to have seriously evaluated), applies or does not apply to RH?
Nov
15
reviewed No Action Needed Intuition for Haar measure of random matrix
Nov
14
reviewed Close What is a maximal set in the context of argumentation in AI
Nov
14
comment Equation $x^2=y^p + 1$
Can those voting to close think about the problem for a few minutes? If they do see a quick solution, I would certainly appreciate knowing about it. (I can see how a proof would go, as indicated in Zudilin's answer below, but it certainly is not immediate.)
Nov
14
reviewed Leave Open Equation $x^2=y^p + 1$
Nov
12
reviewed Close Relationship between quadratic residues modulo a prime and quadratic residues modulo a prime power
Nov
12
comment Show the upper bound of cardinality of $A$ is $C\sqrt{n\log{n}}$
Nicely done, and you took into account the subtlety with primes dividing $\ell$ that I overlooked when writing my comment.