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Find the integers a, b and c such that a^3 + b^3 = 22c^3.

First I did some research from the public library and obtained some lecture notes on Fermat's Last Theorem, but I made little progress, partly because I don't understand most part of the book.

The only thing I know about this equation is that they are all relative primes, and a^3 and b^3 must be odd numbers.

Can somone please show me how this is done?