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2d
comment Collatz property implying infinite “fall below” trajectories, is it known?
OK, so what you are asserting is that for every $m$ there exists $n$ such that for every $a$ $T^k(a\cdot2^n+m)<a\cdot2^n+m$ for some $k$, where $T$ is the Collatz iteration, right?
2d
comment Collatz property implying infinite “fall below” trajectories, is it known?
I think you are claiming that for every $m$ there exists $n$ such that for every $a$ Collatz is true for $a\cdot2^n+m$. Is that right?
2d
comment The Diophantine equation $x^p - 4y^p = z^2$
@Dietrich, there are more where those came from, I think eight examples with $x<1000$.
Aug
20
comment The Diophantine equation $x^p - 4y^p = z^2$
Note that my earlier comment referred to an earlier version of the question.
Aug
20
comment The Diophantine equation $x^p - 4y^p = z^2$
$78^3-4\times29^3=614^2$. $93^3-4\times53^3=457^2$.
Aug
19
comment A conjectured formula for Apéry numbers
@Will, my late colleague, Alf van der Poorten, is also credited as an author of that book.
Aug
19
comment Maximal score for the 2048 game
See also mathoverflow.net/questions/160703/…
Aug
19
comment Expected value when rolling multiple k-sided dice and keeping the highest score and 1s cancelling higest remaining values
MO is for questions of mathematical research. I'm not convinced that this is a research question.
Aug
18
comment Integer valued polynomial through some points with rational coordinates
Please include a link to the m.se question, and include a link there to this question.
Aug
17
comment Linear dependency of real numbers with integer coefficients adding up to zero
There are "integer-relation finding algorithms" around, you might want to do a search for those.
Aug
14
comment Smallest prime in an arithmetic progression
Xylouris has 5.18 in Xylouris, Triantafyllos, On the least prime in an arithmetic progression and estimates for the zeros of Dirichlet L-functions, Acta Arith. 150 (2011), no. 1, 65–91, MR2825574 (2012m:11129).
Aug
14
comment When is a cubic polynomial a cube?
You posted on m.se and MO without linking each to the other. That's rude.
Aug
12
comment Maximum possible number of similar three colored triangles
I suppose for the $2\times2\times2$ you insist on planarity, else the vertices of a regular octahedron will do.
Aug
12
comment Nontransitive dice
See also math.stackexchange.com/questions/57338/…
Aug
12
comment A Conjecture About Directed Graphs that are the Union of Two Trees
Where is the example of Chudnovsky & Seymour?
Aug
12
comment Divisor sums over values of binary forms of primes
Possibly simpler questions would be $$\sum\tau(x^2+y^2)$$ over all $x,y$ up to $n$ (so, not restricting $x,y$ to primes), or $$\sum\tau(p+1)$$ summing over primes $p<n$. Are asymptotics known for these?
Aug
10
awarded  Nice Answer
Aug
8
comment Characterize the set of roots of cubics with certain properties
You may also want to look at mathoverflow.net/questions/21267/…
Aug
8
comment Characterize the set of roots of cubics with certain properties
Pity, that. It's a good book to have, if you are interested in this sort of question. Are there any libraries where you live?
Aug
8
comment Characterize the set of roots of cubics with certain properties
Have you gone through Chapter 7.3 of Alaca and Williams yet?