Maths Blog #149: The curious case of the perfect square 15625, a versatile all-rounder!
Maths Blog #149: The curious case of the perfect square 15625, a versatile all-rounder!
Decided to pen a quick blog thanks to the message from my friend and ex-colleague Prasanna Aravamudhan over the week-end. He forwarded me a note that today's date in DDMMYY (if you ignore the zero!) format is a perfect square. 15/6/25.. 15625 and that acted as a trigger for me to write about 15625 - a true versatile allrounder that each one of us would like to have in our team!
Here are some interesting stats about the number
1. As we know by now, 15625 is a perfect square of 125
2. Remove the leading number 1 and the resultant is 5625 which is also a perfect square of 75!
3. Remove the first 2 digits (15) and the resultant is 625 which is also a perfect square of 25!!
4. Remove the first 3 digits (156) and the resultant is 25 which turns out to be a perfect square of 5!!!
5. 15625 also turns out to be a perfect cube of 25!
Now for some deeper insights on this perfect square
6. The reverse of 15625 (52651) turns out to be a product of two prime numbers - 37 and 1423. Unlike 15625 which has 5 and other factors, 52651 is a odd number with only two prime factors
7. Add 156 and 25 and the outcome is 181 while if we subtract 156 and 25, the resulting number is 131. Both 181 and 131 and palindrome primes!
8. 15625 is sum of multiple perfect squares - 100 ^ 2 + 75 ^ 2, 120 ^ 2 + 35 ^ 2
9. Sum of all the digits of 15625 is 19 which is a prime number
10. Sum of the squares of all the digits of 15625 (1+25+36+4+25) is 91 which is a product of two primes also reverse of 19 in the previous step!!
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