What is the smallest number that can be expressed as the sum of two different cubes in two different ways?

1729
1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

What is the smallest taxicab number?

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is 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 = Ta(2) = 13 + 123 = 93 + 103.

Why is 1729 a magic number?

Discovered by mathemagician Srinivas Ramanujan, 1729 is said to be the magic number because it is the sole number which can be expressed as the sum of the cubes of two different sets of numbers. …

How do I find my taxicab number?

The nth Taxicab number Taxicab(n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Taxicab(2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).

What is the smallest number?

Whole Numbers | Exercise 2.1 The smallest whole number is “0” (ZERO).

Is 1729 a perfect cube?

The number 1729 on prime factorization gives 7 × 13 × 19. Therefore the cube root of 1729 is irrational, hence 1729 is not a perfect cube.

How is 2 a taxicab number?

A taxicab number is the name given by mathematicians to a sequence of special numbers: 2, 1729 etc. A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways.

Is 2 a taxicab number?

The first few taxicab numbers are therefore 2, 1729, 87539319, 6963472309248, 48988659276962496, (OEIS A011541).

What is taxicab geometry used for?

Taxicab geometry can be used to assess the differences in discrete frequency distributions. For example, in RNA splicing positional distributions of hexamers, which plot the probability of each hexamer appearing at each given nucleotide near a splice site, can be compared with L1-distance.

Is taxicab one word or two?

“Taxicab” is a compound word formed from contractions of “taximeter” and “cabriolet”.

What is the smallest positive number?

0 is the smallest positive integer.

What is the smallest integer?

zero
The smallest integer is zero.

What is the taxicab number of 1729?

Taxicab Numbers. The nth Taxicab number Taxicab(n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Taxicab(2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).

Is 1729 the smallest number in the world?

Ramanujan said that it was not. 1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

What is a taxicab number in math?

A taxicab number (the definition that is being used here) is a positive integer that can be expressed as the sum of two positive cubes in more than one way. The first taxicab number is 1729, which is: 1 3 + 12 3 and also 9 3 + 10 3.

What is the nth taxicab number?

The nth Taxicab number Taxicab (n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Taxicab (2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).