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$\begingroup$ Thanks. But the RHS varies as m,n vary so this doesn't represent fixed n? $\endgroup$

joro
– joro

2013-08-08 09:56:35 +00:00
Commented Aug 8, 2013 at 9:56
4

$\begingroup$ Yes, you are right. This identity does not produce infinitely many integer solutions. It only proves Ryley's Theorem that "any non-zero rational number $m$ is the sum of three rational cubes in an infinite number of non-trivial ways.” $\endgroup$

Zurab Silagadze
– Zurab Silagadze

2013-08-08 10:08:06 +00:00
Commented Aug 8, 2013 at 10:08

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