Blog Post #143: Case of Amicable Squares!

In my last blog post, I had written about "Amicable numbers" which has been well documented and researched

Last week, we met for a Team lunch and when I received the bill, I noticed that it was a perfect square! (1764). I have written about 1764 in one of my earlier blog almost 5 to 6 years ago but given the recent topic on amicable numbers, I was wondering if some of the squares like 1764 have something in common and started exploring that further

Guess what - Numbers don't disappoint us any time and I did get to see a peer/counterpart for 1764 which had similar attributes and patterns if not a 100% match

Here we go and look at some interesting points about 1764 and 2916 which i would like to call as "Amicable Squares" for the purpose of this blog

1. To begin with 1764 and 2916 are perfect squares of 42 and 54

2. Both squares are formed by a combination of prime number and another perfect square - 17 and 64, 29 and 16

3. One of the anagram of 1764 is 4761 and similarly 9216 is an anagram of 2916 - Both turn out to be perfect squares again (of 69 and 96) and on top of that, as we could see 69 and 96 are reverse of each other!

4. Another anagram of 1764 turns out to be the famous "Kaprekar constant" - 6714 (More about it could be found through this link (https://en.wikipedia.org/wiki/6174_(number)#:~:text=6174%20is%20known%20as%20Kaprekar's,Kaprekar.)

5. On similar lines, 9261 is an anagram of 2916 and is a perfect cube while 1296 which is another anagram, is a perfect square of 36 which in turn is a perfect square of 6!

6. Replace 64 with 29 to get 1729 which is Ramanujan number again! Cannot leave this magic number out of any number game :)

7. Add the digits of 1764 and 2916 and we would get 18 in both cases!

1764 and 2916 are a great example of perfect squares which demonstrate similar behavior and it would be great fun to see if there are similar square pairs (formed by a combination of prime number and a square)

#NumbersAreFun #PerfectSquares