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COMMENTS
| 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.
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