Henri . Cohen on Sat, 10 Aug 2013 00:30:20 +0200

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Re: x^3 + y^3 = 22 z^3 how to?

To complement Bill's message:

1) If (x,y) is a solution then
is also a solution. Note that this is independent of "22".

2) A consequence of the BSD conjecture is that any squarefree
integer congruent to 4,6,7,8 modulo 9 has the same property
(note 22 = 4 modulo 9).

3) This is not an if and only if statement: there exist
certain squaregree integers not congruent to 4,6,7,8 modulo 9
having that property.

For a modern an extensive study of x^3+y^3=nz^3, see my book
Springer GTM 239 Chapter 6, Section 6.4

Henri Cohen