what is so special with 1729?
Answers
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.
question
Why 1729 is a magic number?
.It is 1729. 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.
Other way to express
1729 = 13 + 123 = 93 + 103
1729 is generally called the Hardy - Ramanujan number, so behind the so called speciality of the number, there's a long story, but I will try my best to explain you briefly and in short. So, it was a time when Ramanujan was granted the membership of the Royal society of the London, while he was teaching and researching on his some topics. After a time, when he became very ill and he got that,he can't live much more, he was admitted in the hospital, after that Professor GH Hardy comes to the hospital for meeting Ramanujan, he came in a taxi with number 1729, the speciality of professor Hardy was that he notes the number of each vehicle he uses, he found something interesting with 1729, but then he called it the Dull number, he came to Ramanujan and told him, then Ramanujan told him that it's indeed interesting, he told Hardy that It's the first number which can be represented as the sum of cube of two numbers in two different ways. You can represent 1729 as the sum of cube of 12 and 1, sum of cube of 10 and 9, so it became the first so number in Mathematics. There are many more numbers also, some of them are 4104 and 13832, which can be represented as the sum of cubes in 4104 as of 16,2 and 9,15 while in 13832 sum of cubes of 18,20 and 24,2. Also, a point should be noted that, it's not necessary that every such number will be a factor of 1729, it can and can't. Both possibilities exist, as 13832 is factor of 1729, while 4104 is not