12,242 reputation
24466
bio website
location
age
visits member for 1 year, 1 month
seen 5 mins ago

Aug
27
comment Dynamics in the integers - Floor function
For the second part use Weyl's equidistribution theorem which shows that the limit is $1-\alpha N$.
Aug
26
reviewed Leave Closed Proof without words for surface area of a sphere
Aug
26
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
I think $k$ is a about size $b$, which is roughly $\ell-m$. Knowing that this is at least $5$ doesn't help, or hurt, the computations of GH from MO. In the notation of the original question, GH from MO's computations have disproved the conjecture if the condition had been $b<a<8b$.
Aug
25
awarded  Nice Answer
Aug
25
reviewed Looks OK if V(f) is irreducible, then how to show that the polynomial f itself is irreducible?
Aug
25
reviewed Close if V(f) is irreducible, then how to show that the polynomial f itself is irreducible?
Aug
25
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
@GHfromMO: Your values seem to give $C$ more like $0.04$ rather than $0.4$? (I mean the $C$ in the $C \log x$ of my answer.) This is why I thought there may be a typo there.
Aug
25
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
@GHfromMO: That's very nice! If we think of a Poisson process, then maybe one expects to find no counterexample around size $10^{10}$ with probability $1/e$, and finding no counterexample of size $10^{20}$ with probability $1/e^2$ etc. Also, I'm not completely sure of the numerical value you give for $C$ -- maybe a typo somewhere? (If $C$ is really as big as $0.4$ wouldn't you expect counterexamples sooner?)
Aug
25
reviewed No Action Needed What is the correct statement of this Erdös-Gallai-Tuza problem generalizing Turan's triangle theorem?
Aug
25
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
added 926 characters in body
Aug
24
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
Note that the heuristic I gave also suggests that apart from finitely many exceptions, the largest square factor of $m^3-2$ is at most $(m\log m)^2$, say. So this is certainly in a very delicate range!
Aug
24
answered Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
Aug
24
reviewed Leave Closed Maximal score for the 2048 game
Aug
24
reviewed Leave Open Repetend digit graphs for $1/n$ in base $b$
Aug
24
reviewed Leave Open Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
Aug
23
comment Smooth sums of coprime smooth integers
@StefanKohl: This is not specified, but could be calculated with some effort. It would likely be quite large.
Aug
23
revised Smooth sums of coprime smooth integers
Reference to recent work added
Aug
23
comment Separation of lattice points on the Mordell elliptic curve
To clarify: your question is not about the difference between $x^3$ and $y^2$ (Hall's conjecture), but rather about the difference between those values of $x$ for which the spacing between $x^3$ and its nearest square is small (below $\sqrt{x}$). Is that correct?
Aug
23
reviewed Leave Closed Aperiodic set of corner Wang Tile
Aug
23
reviewed Close Why calculus textbooks do not include the natural integration constants in the tables of integrals?