In mathematics, the sum of two cubes is a cubed number added to another cubed number. Every sum of cubes may be factored according to the identity a 3...

not the sum of two rational cubes. In real numbers, the cube function preserves the order: larger numbers have larger cubes. In other words, cubes (strictly)...

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...

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...

{n-1}{k}}} ⁠. Sum of two cubes Binomial number Sophie Germain's identity Aurifeuillean factorization Congruum, the shared difference of three squares...

ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes): 91 = 63 + (−5)3 = 43 + 33. (See 1729 for more details)...

that cannot be expressed as a sum of three cubes? More unsolved problems in mathematics In the mathematics of sums of powers, it is an open problem to...

number that is the sum of two cubes in two different ways. Attempting to classify all numbers this way leads to a paradox or an antinomy of definition. Any...

Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize...

prehistory. 1,729 is the smallest number that can be represented as the sum of two cubes in two ways, 1³ + 12³ = 9³ + 10³, serial number 2716057 = (952³ - 951³)...

centered cube number and a heptagonal number. The centered cube numbers are the sums of two consecutive cubes, and 189 can be written as sum of two cubes in...

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...

Heinz, All about Magic Cubes Marian Trenkler, Magic p-dimensional cubes Marian Trenkler, An algorithm for making magic cubes Marian Trenkler, On additive...

polynomial. Sparse polynomials often come up in sum or difference of powers equations. The sum of two cubes states that ( x + y ) ( x 2 − x y + y 2 ) = x...

as the sum of n positive perfect squares)", The On-Line Encyclopedia of Integer Sequences, OEIS Foundation Sum of consecutive cubes equal a cube, archived...

factorization algorithm: algebraic factors of binomial numbers (e.g. difference of two squares and sum of two cubes), which depend on the exponent, and aurifeuillean...

the sum of two cubes in two different ways." Immediately before this anecdote, Hardy quoted Littlewood as saying, "Every positive integer was one of [Ramanujan's]...

(binomial) that was used to define the number, such as difference of two squares and sum of two cubes, there are other prime factors (called primitive prime factors...

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n )...

0-691-07041-5. pp 101–121 Cube classes Christian Boyer: Perfect Magic Cubes Harvey Heinz: Perfect Magic Hypercubes Harvey Heinz: 6 Classes of Cubes Walter Trump:...

as the sum of two positive cubes in two different ways. The first such number, 1729, is called the "Ramanujan–Hardy number". 4104 is the sum of 4096 +...

simplify the expression. For instance using the factorization of the sum of two cubes: 1 a 3 + b 3 = a 2 3 − a b 3 + b 2 3 ( a 3 + b 3 ) ( a 2 3 − a...

six cubes with rotational freedom, three cubes, and five cubes. Two compounds, consisting of two and three cubes were found in Escher's wood engraving print...

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...

is a pentatope number. 126 is a sum of two cubes, and since 125 + 1 is σ3(5), 126 is the fifth value of the sum of cubed divisors function. 126 is the fifth...

interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." Putney is served by mainline South Western Railway...

expressed as the sum of two cubes (of positive numbers) in two different ways. Let C ( X ) {\displaystyle C(X)} denote the number of Carmichael numbers...

corridor, and diagonal passing through the center sums to forty-two. 42 can be expressed as the sum of three cubes: 80 , 435 , 758 , 145 , 817 , 515 3 + 12 ,...

classifications. The magic constant for magic cubes is S = m(m3 + 1)/2. A proper pantriagonal magic cube has 7m2 lines summing correctly. It contains no magic squares...

to the cube's magic constant. Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist, and cubes of orders...