A121234 - OEIS

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A121234

Natural integers x such that x*(x+1)*(x+2)+1 is a square.

0, 2, 4, 55 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`The sequence is finite by Thue's theorem` `n(n + 1)(n + 2) + 1 = n^3 + 3n^2 + 2n + 1. The set of x values of integral solutions to the elliptic curve y^2 = n^3 + 3n^2 + 2n + 1 (see MAGMA program) is { -2, -1, 0, 2, 4, 55 }. So the sequence is complete. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007`
	MAPLE	`(MAGMA) P<n> := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 + 3n^2 + 2n + 1)) ])}; - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007`
	CROSSREFS	`Sequence in context: A018337 A092389 A005274 * A084574 A087621 A062784` `Adjacent sequences: A121231 A121232 A121233 * A121235 A121236 A121237`
	KEYWORD	`fini,nonn,full`
	AUTHOR	`Roger Cuculiere (rcuculiere(AT)free.fr), Aug 21 2006`

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Last modified February 15 16:28 EST 2012. Contains 205823 sequences.