This blog post is dedicated to Dr. Kaprekar constant which is 6174 - More details on that is available at this link - https://en.wikipedia.org/wiki/6174_(number)
Let's look at some more unique characteristics of this number
a) 61 + 74 is 135 and 13x5 is 65. Now 65 - 61 and 74 - 65 are both perfect squares (4 and 9) and 4 + 9 is 13 which is the first 2 digits of 135 and 9 - 4 is 5 which is the last digit!
b) 6174 can be written as (7 ^ 3) * (3 ^ 2) * (2 ^ 1) * (1 ^ 0) - Note that starting from left to right the exponents and indices alternate from 3 to 1
c) Two of the anagrams of 6174 are perfect squares - 4761 and 1764
d) The following takes the cake!
61 + 74 = 135. Add a perfect square to it - 135 + 9 and you get another perfect square - 144.
617 + 4 = 621. Add a perfect square to it - 621 + 4 and you get another perfect square - 625
6 + 174 = 180. Add a perfect square to it - 180 + 16 and you get another perfect square - 196
Let's look at some more unique characteristics of this number
a) 61 + 74 is 135 and 13x5 is 65. Now 65 - 61 and 74 - 65 are both perfect squares (4 and 9) and 4 + 9 is 13 which is the first 2 digits of 135 and 9 - 4 is 5 which is the last digit!
b) 6174 can be written as (7 ^ 3) * (3 ^ 2) * (2 ^ 1) * (1 ^ 0) - Note that starting from left to right the exponents and indices alternate from 3 to 1
c) Two of the anagrams of 6174 are perfect squares - 4761 and 1764
d) The following takes the cake!
61 + 74 = 135. Add a perfect square to it - 135 + 9 and you get another perfect square - 144.
617 + 4 = 621. Add a perfect square to it - 621 + 4 and you get another perfect square - 625
6 + 174 = 180. Add a perfect square to it - 180 + 16 and you get another perfect square - 196
