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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 |
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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 |
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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? |