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A Taxicab number is the smallest positive number that can be expressed as a sum of two positive integer cubes in n distinct ways. The smallest taxicab number after Ta (1) = 1, is Ta (2) = 1729, [4] expressed as. or. Ta (3), the smallest taxicab number expressed in 3 different ways, is 87,539,319, expressed as. , or.
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of can be found using difference of two squares: (since ) Therefore, the linear factors are and . Since the two factors found by this method are complex conjugates, we can use this in ...
A cube with unit side length is the canonical unit of volume in three-dimensional space, relative to which other solid objects are measured. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs.
Manipulative (mathematics education) In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience.
The intersection of any two doubly infinite arithmetic progressions is either empty or another arithmetic progression, which can be found using the Chinese remainder theorem. If each pair of progressions in a family of doubly infinite arithmetic progressions have a non-empty intersection, then there exists a number common to all of them; that ...
With even cubes, there is considerable restriction, for only 00, o 2, e 4, o 6 and e 8 can be the last two digits of a perfect cube (where o stands for any odd digit and e for any even digit). Some cube numbers are also square numbers; for example, 64 is a square number (8 × 8) and a cube number (4 × 4 × 4).
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