Sixth power
In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together.
The sequence of sixth powers of integers are: They include the significant decimal numbers 106 (a million), 1006 (a short-scale trillion and long-scale billion), 10006 (a quintillion and a long-scale trillion) and so on.
The sixth powers of integers can be characterized as the numbers that are simultaneously squares and cubes.
A well-known result in number theory, proven by Rudolf Fueter and Louis J. Mordell, states that, when
[2] In the archaic notation of Robert Recorde, the sixth power of a number was called the "zenzicube", meaning the square of a cube.
[5] There are infinitely many different nontrivial solutions to the Diophantine equation[6] It has not been proven whether the equation has a nontrivial solution,[7] but the Lander, Parkin, and Selfridge conjecture would imply that it does not.
) 3
and (3 2
) 3
, respectively) and as squares ((2 3
) 2
and (3 3
) 2
, respectively)