Because the arrival of the 2025 Has it been greeted with particular enthusiasm by mathematicians? Well, because the number 2025 it is decidedly particular and full of curiosity. Using only the basic notions of arithmetic, in fact, we can write this number in several truly remarkable ways!
First, the number 2025 is a perfect squareor the product of an integer by itself, in this case the number 45:
2025 = 452
The last time a year on our calendar was a perfect square was well 89 years agothat is, to 1936which equals 442. Next time we will have to wait even longer, 91 years to be precise: 2116in fact, is the square of 46.
The number 45, however, is particularly “apt” because it is the sum of 20 And 25. This allows us to write the number 2025 in a very elegant way:
2025 = (20+25)2
But the number 45 is also special for other reasons. It is equivalent, for example, to the sum of all the digits from 0 to 9: in other words, 45 = 0+1+2+3+4+5+6+7+8+9. This means 2025 is the square of the sum of all the digits of the decimal system:
2025 = (0+1+2+3+4+5+6+7+8+9)2
And it doesn’t end there, because there is another way to write 2025 using all the digits from 0 to 9. Let’s first take the cubes of all the digits, that is, the same digits raised to the third, for example 23 = 2·2·2 = 8 or 33 = 3·3·3 = 27. If we now add all the results, we get – guess what! – precisely the number 2025:
2025 = 03+13+23+33+43+53+63+73+83+93
Do you still want mathematical coincidences about 2025? Here you are served: 2025 can be written as the product of two perfect squaresthat is, the squares of 9 and 5:
2025 = 92·52
(obtained from the fact that 45 = 9·5) and also as the sum of three perfect squaresi.e. the squares of 40, 20 and 5:
2025 = 402+202+52
