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A152463
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Numbers k such that 4 + 5*k^3 is a square.
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0
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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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]
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PROG
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(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
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CROSSREFS
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Sequence in context: A083284 A350613 A152218 * A295206 A209608 A159367
Adjacent sequences: A152460 A152461 A152462 * A152464 A152465 A152466
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KEYWORD
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fini,full,nonn
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AUTHOR
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Zak Seidov, Dec 05 2008
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STATUS
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approved
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