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Four special squares (Posted on 2014-01-30) Difficulty: 3 of 5
There are only four squares that are equal to the sum of three consecutive cubes.

Zero is one of them.

Find the other three.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re(3): solutions Comment 5 of 5 |
(In reply to re(2): solutions by Benny)

a quote from OEIS:

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. - Jaap Spies, May 27 2007

  Posted by Ady TZIDON on 2014-01-30 19:55:09
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