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### Ramanujan Magic Number Riddle

Ramanujan Magic Number Riddle - 22 July

Ramanujan discovered 1729 as a magic number.

Why 1729 is a magic number ?

1. 1729 is the smallest number that can be expressed as the sum of cubes of two different numbers in two different ways.
1729 = 10ᶟ + 9ᶟ
1729 = 12ᶟ + 1ᶟ

2. it is the smallest 'positive' number that can be expressed as a sum of two cubes in two different ways.The smallest number is 93
3^3+4^3=93
-5^3+6^3=93

3. Lol....
3^3 + 4^3 is 91
But should be expressed as sum of 2 positive cubes..

2. sum of cubes of two different numbers in two different ways.
10^3+9^3=1729
12^3+1^3=1729

3. 1729 is the lowest number that is a sum of 2 cubes and can be expressed in two ways:
1729=1728+1
1729=1000+729

4. 1729 is the product of two primes i.e 13 and 133

1729= 13 *133.
It is also product of two peculiar Numbers, (where, one number can be obtained by simply interchanging the digits of other Number)

1729 = 19 * 91

1. 1729 = 7 ×13 × 19
Product of 3 prime numbers

5. Sorry. 133 is not a prime though.These two are funny numbers.We get 133, by adding '3' to the right of '13' Or get '13' by removing any '3' from '133'.
Our 1729 is perhaps considered a magic Number. because it is the Product of '13' and '133'.

6. 1 + 7 + 2 + 9 = 19
19 × 91 = 1729