The New Sudoku Players' Forum

[Serg]

Hi, people!
My friend sent me amazing mathematical observations (I don't know who is the author of these formulae). Sign "^" denotes "power" sign.

2025 = (20 + 25)^2
2025 = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)^2
2025 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3

Serg

[rjamil]

Perfect square:
The year 2025 holds a unique mathematical distinction as a "perfect square year," being the square of 45 (45 x 45 = 2025). This is a relatively rare occurrence, with the last one being 1936 (44 x 44) and the next one being 2116 (46 x 46).

Sum of Three Squares:
40² + 20² + 5² = 2025

Product of Squares:
9² * 5² = 2025

Harshad Number:
(also known as a Niven number), meaning it is divisible by the sum of its digits (2+0+2+5 = 9),

R. Jamil

[Serg]

Hi, Jamil!
Property "2025 = (20 + 25)^2" is extremely rare. Let's call such years, having even number of digits, "balanced". It's turn out, there are only 3 such 4-digit years: 2025, 3025, 9801. Not every millenium contains such "balanced" years.

Serg

[rjamil]

2025 as the 23rd Centered Octagonal Number:
These numbers represent a geometric pattern where a point is placed at the center, and subsequent layers of dots form an octagon around it.

The formula for the nth centered octagonal number is 1 + 8 * (n * (n - 1) / 2). For n=23, this formula calculates to 1 + 8 * (22 * 23 / 2) = 1 + 8 * 253 = 2025.

R. Jamil

[Leren]

I think you have missed an "important" one. It's part of a Pythagorean Triple (sum of two squares and is a square) : 27^2 + 36^2 = 45^2 = 2025.

or even maybe the sum of a power of six and one of 4 and is a square : 3^6 + 6^4 = 45^2 = 2025

or even 2025 = 401 + 403 + 405 +407 +409.

In date form two dates in the year 2025 i.e. 9/12/2025 or 12/9/2025 form part of a Pythagorean Quadruple : 9^2 + 12^2 + 20^2 = 25^2

Other Pythagorean dates in 2025 are 24/7/2025, just a few days ago, which is part of the Pythagorean Triple 7^2 + 24^2 = 25^2 - a so called limping square Pythagorean Triple.

or in about a month's time 4/9/25 is related to the most well known Pythagorean Triple of them all 3^2 + 4^2 = 5^2.

Leren

[rjamil]

The Prime Factorization:
3 x 3 x 3 x 3 x 5 x 5 = 3⁴ × 5² = 2025

R. Jamil