A152463 Numbers k such that 4 + 5*k^3 is a square.

0, 1, 4, 532

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

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]

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

Adjacent sequences: A152460 A152461 A152462 * A152464 A152465 A152466

Keyword

fini,full,nonn

Author

Zak Seidov, Dec 05 2008

Status

approved