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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.