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A152463 Numbers n with the property that 4 + 5n^3 is a square. 0
0, 1, 4, 532 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

Table of n, a(n) for n=1..4.

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]

EXAMPLE

4 + 5n^3 = s^2, s = 2,3,18,27438.

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)] [From Vincenzo Librandi, Dec 16 2010]

CROSSREFS

Sequence in context: A257922 A083284 A152218 * A209608 A159367 A012770

Adjacent sequences:  A152460 A152461 A152462 * A152464 A152465 A152466

KEYWORD

fini,full,nonn

AUTHOR

Zak Seidov, Dec 05 2008

STATUS

approved

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Last modified September 24 18:42 EDT 2017. Contains 292433 sequences.