New Seq: Differences between squares are cubes

Maximilian Hasler Maximilian.Hasler at martinique.univ-ag.fr
Thu Apr 10 16:30:40 CEST 2008


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)) }





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