My learned friend Prab Bhatt sent me some amazing 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.
Notice that 45 is the sum of the two parts 20 and 25 in 2025.
(Other numbers that show this property of being chopped in equal parts, and the parts added and squared to yield the same number are 81, 3025, 9801 - try them!)
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
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
