Page 9b: Equal Sums of Like Powers (Cubics) | |||||||||||||||||||||||||||||
"The Equation q1^3 + q2^3 + q3^3 + q4^3 = (a^3 + b^3 + c^3 + d^3)q5^3 In Quadratic Forms" This is a very short paper that is the epilogue to "Ramanujan and the Cubic Equation 3^3+4^3+5^3 = 6^3". Previously, we gave four identities, two of which were general cases. In this continuation, by slightly modifying the expressions for one formula, we give an even more general identity that contains all four. The significance of parametric n-tuple identities like these (see also the limited quartic version in Page 10) is that given one solution to a cubic n-tuple a1^3 + a2^3 + ... + (a_n)^3 = 0, then it automatically proves there is an infinite number of solutions, without having to resort to scaling or multiplying by some common factor. |
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Choose your format: | |||||||||||||||||||||||||||||
FinalCube.htm | |||||||||||||||||||||||||||||
FinalCube.pdf | |||||||||||||||||||||||||||||
See also the new addition to: | |||||||||||||||||||||||||||||
http://mathworld.wolfram.com/DiophantineEquation3rdPowers.html | |||||||||||||||||||||||||||||
Page 10 | |||||||||||||||||||||||||||||
Page 9 | |||||||||||||||||||||||||||||
Index | |||||||||||||||||||||||||||||
This webpage was born Sept 22, 2005 | |||||||||||||||||||||||||||||