This is my 100th Blog post and what could be better than dedicate this to my all time favourite (Ramanujan Number - 1729)
1) Let's start with the Year 2018 - 2018 is sum of 1729 and 289 which a perfect square of 17 (first 2 digits of 1729 as well)!
2) 172 * 9 is 1548 and 172 + 9 is 181 - The difference between 1729 and 1548 is 181 as well!
3) Sum of the digits of 1729 is 19 (1+7+2+9) and when you multiply 19 by its reverse (91) you get 1729 again!
4) Let's now look at some of the anagrams of 1729 and see the properties they exhibit as sum of two perfect squares with one of them being 1 (similar to 1729 which is sum of 12 ^ 3 + 1 ^ 3)
- 1297 is 36 ^ 2 + 1 ^ 2
- 9217 is 96^ 2 + 1 ^ 2
- 2917 is 54 ^ 2 + 1 ^ 2
5) Square of 17 is 289 and square of 289 is 841. Now look at square 1729 which turns out to be 29,89,441. 289 and 841 are subsets of 29,89,441 and there is a visible pattern seen
6) 1729 is 12 ^ 3 + 1 ^ 3 as we are all aware. Now (12+1) ^ 3 is 2197 which is an anagram of 1729!
7) Multiple the 2nd and 3rd digits with 1st and 4th digits (72 x 19) and we get 1368. Now 1729 - 1368 = 361 which is again 19 ^ 2! (square of the 1st and 4th digit)
8) Ramanujan lived between 1887 and 1920... Now look at how these two years combine with his magic number and exhibit an unique property
1729 + 1887 -----> 3616 (6 ^ 2 and 4 ^ 2)
1729 + 1920 -----> 3649 (6 ^ 2 and 7 ^ 2)
9) 1729 is a multiple of 3 distinct prime numbers namely 7, 13, 19. Now let's look at the number 17299271 is formed by appending 9271 (exact reverse of 1729) to the number itself. 17299271 is also a multiple of 4 distinct prime numbers 11, 31, 97, 523!
There are many more such interesting patterns which we could continue to unearth and this just reflects the sheer brilliance of Shri Ramanujan
1) Let's start with the Year 2018 - 2018 is sum of 1729 and 289 which a perfect square of 17 (first 2 digits of 1729 as well)!
2) 172 * 9 is 1548 and 172 + 9 is 181 - The difference between 1729 and 1548 is 181 as well!
3) Sum of the digits of 1729 is 19 (1+7+2+9) and when you multiply 19 by its reverse (91) you get 1729 again!
4) Let's now look at some of the anagrams of 1729 and see the properties they exhibit as sum of two perfect squares with one of them being 1 (similar to 1729 which is sum of 12 ^ 3 + 1 ^ 3)
- 1297 is 36 ^ 2 + 1 ^ 2
- 9217 is 96^ 2 + 1 ^ 2
- 2917 is 54 ^ 2 + 1 ^ 2
5) Square of 17 is 289 and square of 289 is 841. Now look at square 1729 which turns out to be 29,89,441. 289 and 841 are subsets of 29,89,441 and there is a visible pattern seen
6) 1729 is 12 ^ 3 + 1 ^ 3 as we are all aware. Now (12+1) ^ 3 is 2197 which is an anagram of 1729!
7) Multiple the 2nd and 3rd digits with 1st and 4th digits (72 x 19) and we get 1368. Now 1729 - 1368 = 361 which is again 19 ^ 2! (square of the 1st and 4th digit)
8) Ramanujan lived between 1887 and 1920... Now look at how these two years combine with his magic number and exhibit an unique property
1729 + 1887 -----> 3616 (6 ^ 2 and 4 ^ 2)
1729 + 1920 -----> 3649 (6 ^ 2 and 7 ^ 2)
9) 1729 is a multiple of 3 distinct prime numbers namely 7, 13, 19. Now let's look at the number 17299271 is formed by appending 9271 (exact reverse of 1729) to the number itself. 17299271 is also a multiple of 4 distinct prime numbers 11, 31, 97, 523!
There are many more such interesting patterns which we could continue to unearth and this just reflects the sheer brilliance of Shri Ramanujan
