1,2

m^3+(m+1)^3+(m+2)^3=3(1+m)*(3+2*m+m^2). Corresponding values of m are -1,0,1,23.

Comment from Jaap Spies (j.spies(AT)hccnet.nl), May 27 2007: The equation s^2 = 3c^3 + 6c can be transformed using the substitution X = 3c, Y = 3s into Y^2 = X^3 + 18X, a form of the Weierstrass equation of an elliptic curve: Y^2 = X^3 + aX^2 + bX + c, with a = c = 0. We can now use the SAGE program to show that the there are no other integer solutions.

Comment from Warut Roonguthai (warut822(AT)gmail.com), May 28 2007: Confirmed by MAGMA - see code below.

(MAGMA) IntegralPoints(EllipticCurve([18, 0]));

Cf. A027602.

Sequence in context: A079655 A053949 A071134 this_sequence A091961 A103758 A126914

Adjacent sequences: A116105 A116106 A116107 this_sequence A116109 A116110 A116111

fini,nonn,full

Zak Seidov (zakseidov(AT)yahoo.com), Apr 14 2007