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A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:
Geometrically speaking, a positive integer m is a perfect cube if and only if one can arrange m solid unit cubes into a larger, solid cube. For example, 27 small cubes can be arranged into one larger one with the appearance of a Rubik's Cube, since 3 × 3 × 3 = 27. The difference between the cubes of consecutive integers can be expressed as ...
Alternatively, one can decompose the table into a sequence of nested gnomons, each consisting of the products in which the larger of the two terms is some fixed value. The sum within each gmonon is a cube, so the sum of the whole table is a sum of cubes. [7] Visual demonstration that the square of a triangular number equals a sum of cubes.
1729 can be expressed as a sum of two positive cubes in two ways, illustrated geometrically. 1729 is also known as Ramanujan number or Hardy–Ramanujan number, named after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan who was ill in a hospital.
1728 is the cube of 12, [2] and therefore equal to the product of the six divisors of 12 (1, 2, 3, 4, 6, 12). [3] It is also the product of the first four composite ...
Srinivasa Ramanujan (picture) was bedridden when he developed the idea of taxicab numbers, according to an anecdote from G. H. Hardy.. In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. [1]
172 is a part of a near-miss for being a counterexample to Fermat's last theorem, as 135 3 + 138 3 = 172 3 − 1. This is only the third near-miss of this form, two cubes adding to one less than a third cube. [1] It is also a "thickened cube number", half an odd cube (7 3 = 343) rounded up to the next integer. [2]
216 (two hundred [and] sixteen) is the natural number following 215 and preceding 217. It is a cube , and is often called Plato's number , although it is not certain that this is the number intended by Plato .