New Seq: Differences between squares are cubes

[Jack Brennen]

Google for MWRANK -- it's a program for analyzing these type
of elliptic curves.  If someone has a faster machine or more
patience, and wants to try to run MWRANK on this curve, you
might try it.  I let a very old version of the program crunch
on it for about an hour last night with no significant progress.
There might be some tweaking of the program needed due to the
size of the coefficient, I just don't know.

Anyway, do this:

  echo '0 0 0 0 61178957256694622500' | mwrank

(The big number there being a(42)^2 ...)

I don't claim to know all that much about mwrank, or how to
analyze its output.

If anyone uses SAGE, apparently SAGE has MWRANK built in (?).


   Jack

Maximilian Hasler wrote:
> nice citation! via this one, I also found:
> 
> A. Baker: "Contributions to the Theory of Diophantine Equations. II.
> the Diophantine Equation y2 = x3 + k",
> Philosophical Transactions of the Royal Society of London. Series A,
> Mathematical and Physical Sciences, Vol. 263, No. 1139 (Jul. 18,
> 1968), pp. 193-208
> 
> Maximilian
> 
> PS: until we derive from these papers that a(42) is indeed the last term,
> if someone intends to push the search further, may I suggest a
> slightly simplified version of Richard's code, which is 3x faster:
> (apologies in advance to those offended by potentially unreadable
> code...)
> 
> { a=1; while( 1, print1(a",");
> a2=a^2; q=floor(a^(1/3)); until( issquare(a2+q++^3),); a=sqrtint(a2+q^3)) }
> 
>