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A152463
Numbers k such that 4 + 5*k^3 is a square.
0
OFFSET
1,3
COMMENTS
The corresponding squares are 2^2, 3^2, 18^2, and 27438^2.
Multiplying by 5^2 and making the substitution x' = 5x, y' = 5y we get a Mordell curve y'^2 = x'^3 + 100, for which we can find solutions in one of the text files at the J. Gebel link. We are interested in solutions divisible by 5, and up to a sign there are only 4 of them. So the list is complete. - Max Alekseyev, Dec 05 2008
LINKS
J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
MATHEMATICA
Select[Range[0, 600], IntegerQ[Sqrt[4+5#^3]]&] (* Harvey P. Dale, Oct 31 2024 *)
PROG
(PARI) {for(x=0, 2*10^9, if(issquare(4+5*x^3, &y), print(x", "y)))}
(Magma) [n: n in [0..1000]|IsSquare(4+5*n^3)] // Vincenzo Librandi, Dec 16 2010
CROSSREFS
Sequence in context: A083284 A350613 A152218 * A295206 A209608 A159367
KEYWORD
fini,full,nonn,changed
AUTHOR
Zak Seidov, Dec 05 2008
STATUS
approved