22,837 reputation
36098
bio website
location
age
visits member for 3 years, 8 months
seen 8 mins ago

26m
answered Exponential Sum Bound
48m
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
deleted 10 characters in body
10h
revised Dynamics in the integers - Floor function
added 71 characters in body
10h
revised Dynamics in the integers - Floor function
added 71 characters in body
10h
comment Dynamics in the integers - Floor function
@Lucia: I just wrote the same. But you probably beat me by a minute or so.
10h
revised Dynamics in the integers - Floor function
added 368 characters in body
10h
answered Dynamics in the integers - Floor function
11h
comment What does a Turing machine compute?
See also en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis
18h
awarded  Nice Answer
21h
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
added 201 characters in body
22h
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
@KierenMacMillan: Yes, this is why I kept the previous example of $0.485$ as well.
22h
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
@Joël: Thanks for your comment. I will update the text accordingly.
22h
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
added 6 characters in body
22h
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
added 89 characters in body
1d
revised Counterexample to Pólya's conjecture
edited body
1d
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
added 8 characters in body
1d
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
deleted 7 characters in body
1d
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
Consider the odd pairs $(\ell,m)$ satisfying $\ell^2\mid m^3-2$. Then the ratios $m/\ell$ are equidistributed in $(0,\infty)$ in a certain sense (I can be more specific if you wish). In particular, the ratios $m/\ell$ are dense in $(0,\infty)$, hence they are infinitely often smaller than $1/3$.
1d
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
@KierenMacMillan: One counterexample does not tell much, beyond disproving your conjecture of course. Infinitely many counterexamples would tell that the abc conjecture cannot be strengthened in a certain way. At any rate, here is a conjecture that I believe is true and would yield infinitely many counterexamples to your conjecture (continued in next comment):
1d
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
We are now at $m/\ell\approx 0.485$ which is smaller than all previous ratios, including the one for $(\ell,m)=(5,3)$.