

A152463


Numbers n with the property that 4 + 5n^3 is a square.


0




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



