positive numbers representable in minimum 2 ways as a sum of positive cubes

Taxicab numbers are the positive numbers representable in minimum 2 ways as a sum of positive cubes.

the smallest number expressible as the sum of two cubes in different ways

In honor of the Ramanujan-Hardy conversation, the smallest number expressible as the sum of two cubes in different ways is known as the taxicab number and is denoted as .

the smallest number which can be written as the sum of x, yth powers in z different ways

The general form for a taxicab number (x,y,z) means the smallest number which can be written as the sum of x, yth powers in z different ways.