The New Year 2025: 2025 is an Amazing Number

My learned friend Prab Bhatt had talked to me about some interesting properties of the number 2025 - the new year that has just started. I share these with some additions:

2025 is a perfect square:  2025 = 45 x 45

In our times, years that are perfect squares happen about once a century.  The previous square year was 1936, and the next will be 2116 - 91 years later.  

Curiously, 2025 is made up of 20 and 25 which add to give 45 - square root of 2025!

2025 is the sum of three squares:  we can write 2025 as follows

                    2025 =  5² + 20² + 40² 

2025 is the product of two squares:  we can write 2025 as follows

                    2025 = 9² x 5² = 3² x 15²

2025 is the sum of cubes of all the digits from 1 to 9:  we can write 2025 as follows

The next year that is the sum of cubes of digits from 1 to 10 will be 3025 - 1000 years later.  Previously, 1296 was the year that was the sum of cubes of digits from 1 to 8!

2025 is the square of the sum of digits from 1 to 9

2025 = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9)²

This makes 2025 square of a triangular number, namely 45.  

While 2025 is not a triangular number itself, it is the sum of the 44th and 45th triangular numbers (990 and 1035).

2025 is interesting:  The sum of digits of 2025 is equal to 9.  

                               2 + 0 + 2 + 5 = 9

We can divide 2025 by 3 and the sum of digits of the quotient is again equal to 9. 

2025  ÷ 3 = 675.  Sum of digits of 675 is 6 + 7 + 5 = 18 

                              and the sum of digits in 18 is 9

And again:  675  ÷ 3 = 225.  Sum of digits of 225 is 2 + 2 + 5 = 9 

2025 and number 7:  If we break number 7 in its odd and even parts we have 

                       7 = 6 +1 = 4 + 3  = 2 + 5.  

The product of odd parts raised to the corresponding even part gives

Happy New Year!