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of the form or (since they are infinite families of solutions), satisfies , and has minimal values for and (tested in this order).

Only primitive solutions are selected since the non-primitive ones can be trivially deduced from solutions for a smaller value of . For example, for , the solution results from the solution by multiplying everything by Therefore, this is another solution that is selected. Similarly, for , the solution is excluded, and this is the solution that is selected.

Fermat's Last Theorem for cubes

The

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