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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: Cabtaxi (3), the smallest Cabtaxi number expressed in 3 different ways, is 4104 ...
In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum. A necessary condition for an integer to equal such a sum is that cannot equal 4 or 5 modulo 9, because the cubes modulo 9 are 0, 1, and −1, and ...
The sum within each gmonon is a cube, so the sum of the whole table is a sum of cubes. Visual demonstration that the square of a triangular number equals a sum of cubes. In the more recent mathematical literature, Edmonds (1957) provides a proof using summation by parts.
Cube (algebra) y = x3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3. The cube is also the number ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2] Since the problem had withstood the attacks of ...
t. e. In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
In mathematics, the n th 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] The most famous taxicab number is 1729 = Ta (2) = 1 3 + 12 3 = 9 3 + 10 3, also known as the Hardy-Ramanujan number. [2][3]
Andrew Booker (mathematician) Andrew Richard Booker (born 1976) [1] is a British mathematician who is currently Professor of Pure Mathematics at the University of Bristol. [2] He is an analytic number theorist known for his work on L-functions of automorphic forms [3] and his contributions to the sums of three cubes problem. [4][5]
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