As I drove back home on Friday evening from office got a glimpse of 3249 at couple of places - Car registration number ahead of me, a prize tag on one of the online sites and that's when I decided this Blog is on 3249 and its offshoots!
a) For starters, 3249 is a perfect square and that's one reason this caught my attention - 57 x 57
b) 32 + 49 is 81 which is a perfect square of 9. Now if we add the first 3 digits we get 9 and multiply it with the last digit will give us 81 again
c) 324 (first 3 digits) is a perfect square (18 ^ 18) and 9 (last digit) is a perfect square)
d) 32 is 2 ^ 5 and 49 is 7 ^ 2. Now let's flip that - 5 ^ 2 (instead of 2 ^ 5) and 2 ^ 7 (instead of 7 ^ 2). Add the resultant - 25 + 128 = 153 which is Armstrong number!
e) 32 ^ 2 is 1024 and 49 ^ 2 is 2401 - 1024 and 2401 are both anagrams - Voila!
f) For all the factors, squares that 3249 exhibited till now, look at this - Prefix 1 to the number and you get 13249 which is a Prime. Suffix 1 and the resultant (32491) is a prime again!
a) For starters, 3249 is a perfect square and that's one reason this caught my attention - 57 x 57
b) 32 + 49 is 81 which is a perfect square of 9. Now if we add the first 3 digits we get 9 and multiply it with the last digit will give us 81 again
c) 324 (first 3 digits) is a perfect square (18 ^ 18) and 9 (last digit) is a perfect square)
d) 32 is 2 ^ 5 and 49 is 7 ^ 2. Now let's flip that - 5 ^ 2 (instead of 2 ^ 5) and 2 ^ 7 (instead of 7 ^ 2). Add the resultant - 25 + 128 = 153 which is Armstrong number!
e) 32 ^ 2 is 1024 and 49 ^ 2 is 2401 - 1024 and 2401 are both anagrams - Voila!
f) For all the factors, squares that 3249 exhibited till now, look at this - Prefix 1 to the number and you get 13249 which is a Prime. Suffix 1 and the resultant (32491) is a prime again!
