Happy new year from WMS!

As 2024 draws to a close, we hope you’ve had a restful winter break. Happy new year from all of us at Warwick Maths Society! We can’t wait to see you all again in term 2.

Mathematical Miscellany

2025 is a particularly exciting year for us mathematicians because it is a square number; the previous square year was 1936 and the next will be 2116. Here are a few other numerical facts about 2025:

• \(2025\) is the sum of two squares: \(27^2+36^2\);
• \(2025\) is the sum of three squares: \(40^2+20^2+5^2\);
• \(2025\) is the product of two squares: \(9^2\times5^2\), or three, if we allow \(1^2\);
• \(2025=(20+25)^2\);
• \(2025\) is the product of the proper divisors of its square root, \(45\): \(2025=1\times3\times5\times9\times15\);
• \(2025\) is the square of a triangular number (whose index is square!): \(2025=T_9^2=T_{3^2}^2\). Of course, \(3\) is also the second triangular number: \(2025=T_{T_2^2}^2\);
• \(2025=\left(\sum_{n=1}^{9}n\right)^2=\sum_{n=1}^{9}n^3\);
• The digital root of \(2025\) is also square: \(2+0+2+5=9=3^2\);
• \(2025\) is powerful, meaning that, if a prime \(p\) divides 2025, then \(p^2\) also divides 2025.
• Years 2024 and 2025 is the second time the year has been a tetrahedral number (2024) followed by a square number (2025);¹ the next time will be 2600 and 2601.