My earlier post a week ago, was around welcoming 2025 and when I started thinking about what should be the next blog about, I did not have to spend lot of time - Enter the ever versatile and amazing Armstrong number 153!
153 is the first and smallest Armstrong number and it is special in many ways and I was sure that somewhere there is a link between 153 and the perfect square year of this millenium - 2025
Let's see how special 153 is before establishing the link with 2025
a) For starters 153 is an Armstrong number and hence sum of the cubes of its digits equal the number itself
b) 153 is the sum of two squares 12 ^ 2 and 3 ^ 2 as well as difference of two squares 13 ^ 2 and 4 ^ 2!
c) 153 can be written as (9 ^ 2) + 72 as well as (15 ^ 2) - 72 - WOW!
Now let's look at what happens when 153 is flipped over - we get 351 which is not an Armstrong number but watch these similarities between 153 and 351
d) 351 can be written as 18 ^ 2 + 3 ^ 3 as well as 20 ^ 2 - 7 ^ 2
e) Anagrams of 153 are 135 and 315 as well and guess what.. 135 is difference of two squares 12 ^ 2 - 3 ^ 2 and 315 is difference of two squares as well 18 ^ 2 - 3 ^ 2!!
Now finally...
f) 153 + 351 gives 504 which is the lowest 3 digit number that has factors from 1 to 9 except 5
When we multiply 504 with 5 we get the magic number 2520, which is the smallest 4 digit number with factors from 1 to 10.
One of the anagram of 2520 is 2025 - Our perfect square year!
Welcome 2025 again!
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