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Sum of four cubes problem, whether every integer is a sum of four cubes; Euler's sum of powers conjecture § k = 3, relating to cubes that can be written as a sum of three positive cubes; Plato's number, an ancient text possibly discussing the equation 3 3 + 4 3 + 5 3 = 6 3; Taxicab number, the smallest integer that can be expressed as a sum of ...
Euler was aware of the equality 59 4 + 158 4 = 133 4 + 134 4 involving sums of four fourth powers; this, however, is not a counterexample because no term is isolated on one side of the equation. He also provided a complete solution to the four cubes problem as in Plato's number 3 3 + 4 3 + 5 3 = 6 3 or the taxicab number 1729.
The sum of cubes of numbers in arithmetic progression is sometimes another cube. The Fermat cubic, in which the sum of three cubes equals another cube, has a general solution. The power sum symmetric polynomial is a building block for symmetric polynomials.
For all of the recent strides we’ve made in the math world—like a supercomputer finally solving the Sum of Three Cubes problem that ... as sums of primes, not less. Like how 3+5 is the only ...
23 = 2 3 + 2 3 + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 + 1 3. In rational numbers Every positive rational number is the sum of three positive rational cubes, [ 9 ] and there are rationals that are not the sum of two rational cubes.
The sum of four cubes problem [1] asks whether every integer is the sum of four cubes of integers. It is conjectured the answer is affirmative, but this conjecture has been neither proven nor disproven. [2] Some of the cubes may be negative numbers, in contrast to Waring's problem on sums of cubes, where they are required to be positive.
Numberphile has produced three YouTube videos related to sums of three cubes in which Andrew Booker is the featured guest: 42 is the new 33; The Mystery of 42 is Solved; 3 as a sum of 3 cubes; As of January 2023 these videos had accumulated a total of almost two million views. [15]
The title is "Sums of three cubes", but the subject is "The mathematical problem commonly called, Sums of three cubes". With research papers the title and subject are usually the same for example, "Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33". Comfr 22:27, 7 August 2023 (UTC)