Unsolved problem in mathematics Is every integer the sum of four perfect cubes? More unsolved problems in mathematics The sum of four cubes problem asks whether...

Unsolved problem in mathematics Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes? More unsolved problems in...

are the sum of three not necessarily positive cubes Sums of four cubes problem, discusses whether every integer is the sum of four cubes of integers...

three-dimensional space, having four cubes around each edge. Compound of cubes is the polyhedral compounds in which the cubes are sharing the same centre...

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...

9 is the sum of the cubes of the first two non-zero positive integers 1 3 + 2 3 {\displaystyle 1^{3}+2^{3}} which makes it the first cube-sum number greater...

hyper cubes be unified into one d-dimensional hyper cube. Assuming a duplex communication model where the σ of two adjacent PEs in different hyper cubes can...

smallest number expressible as the sum of two cubes in two different ways". This conversation led to the definition of the taxicab number as the smallest...

the sum of inverse squares Apéry's constant, the sum of inverse cubes Large set Sum of squares Sums of powers Unless given here, references are in the...

developed software cubes use coloured facelets as for hardware cubes. The most common, but by no means universal, approach is to emulate the cube by providing...

exponents appearing in the problem from squares to cubes, or higher. The dot planimeter is physical device for estimating the area of shapes based on the same...

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every nonnegative integer can be represented as a sum of four non-negative...

{\displaystyle S_{1}=1.} Also, the square of the nth triangular number is the same as the sum of the cubes of the integers 1 to n. This can also be expressed...

ab-3b^{2})^{3}=(6a^{2}-4ab+4b^{2})^{3}} A cube as the sum of three cubes can also be parameterized in one of two ways: a 3 ( a 3 + b 3 ) 3 = b 3 ( a 3...

defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729...

University of Bristol and Andrew Sutherland at Massachusetts Institute of Technology (MIT) used Charity Engine to solve the sums of three cubes problem for the...

the second to last number less than 100 whose representation as a sum of three cubes was found (in 2019): 33 = 8866128975287528 3 + ( − 8778405442862239...

sum _{i}x_{i}&&=\sum _{i}\tan \theta _{i}\\[6pt]e_{2}&=\sum _{i<j}x_{i}x_{j}&&=\sum _{i<j}\tan \theta _{i}\tan \theta _{j}\\[6pt]e_{3}&=\sum...

that the value of Plato's number is 216 because it is the cube of 6, i.e. 63 = 216, which is remarkable for also being the sum of the cubes for the Pythagorean...

generic problem with eight solution circles, The reciprocals of the radii of four of the solution circles sum to the same value as do the reciprocals of the...

sum of four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317) and a Harshad number. Nearly all of the...

Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A343971 (Numbers that are the sum of four positive cubes in four or more...

Sumer (/ˈsuːmər/) is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during...

integers can be written as the sum of three perfect cubes? Can every integer be written as a sum of four perfect cubes? Agoh–Giuga conjecture on the Bernoulli...

the sum of at most 19 fourth powers; every integer larger than 13792 can be expressed as the sum of at most 16 fourth powers (see Waring's problem). Fermat...

following 7999 and preceding 8001. 8000 is the cube of 20, as well as the sum of four consecutive integers cubed, 113 + 123 + 133 + 143. The fourteen tallest...

tetrahedral number 2025 = 452, square of the sum of the first nine positive integers (and therefore sum of the cubes of the first nine positive integers,...

sum of at most five prime numbers (as a lower limit). Unsolved problem in mathematics Is 5 the only odd, untouchable number? More unsolved problems in...

preceding 801. It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number, an Achilles number and the area of a square with diagonal...

solve the entire cube. Given a random cube C, it is solved as iterative deepening. First all cubes are generated that are the result of applying 1 move...