Which numbers can be expressed as sum of two cubes in two different ways?
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.
Which numbers can be written as the sum of two cubes?
1729 is the smallest number which can be expressed as the sum of two cubes in two different ways: 1³ + 12³ and 9³ + 10³.
Can you work out the sum of cubes in two different ways which equals 1729?
He said it is the smallest number that can be expressed as a sum of two cubes in two different ways: 1729 = 1728 + 1 = 123 + 13 1729 = 1000 + 729 = 103 + 93 1729 has since been known as the Hardy – Ramanujan Number, even though this feature of 1729 was known more than 300 years before Ramanujan.
Can the sum of two cubes be a cube?
It is known that one cannot write an integer cube as a sum of two integer cubes (Fermat’s Last Theorem). The number 1728 (= 123) comes close to being the sum of two cubes, but falls short by 1. An entry in Srinivasa Ramanujan’s Lost Notebook gives a remarkable identity which provides infinitely many such examples.
What is the sum of cubes?
Sum or Difference of Cubes A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 is called a difference of cubes.
Which expression is the sum of cubes?
A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 is called a difference of cubes.
What is the value of infinity by Ramanujan?
-1/12
For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.