Back

The new year is one of my favorite kinds of numbers: a difference of squares!

$$2024=(45+1)\times (45-1)={45}^2-1^2$$

This observation got me thinking about what kinds of numbers can be written as the difference of squares. For example, $3=2^2-1^2,5=3^2-2^2$, and $16=4^2-0^2$, but it is impossible to write 6 as the difference of squares of integers.

So here’s a little mathematical puzzle to start the new year: Is there a largest number that can not be expressed as the difference of squares? If so, find it. If not, prove no such number exists. Good luck, and happy new year!

https://mrhonner.com/archives/21614

#Math #NumberTheory #2024 #NewYear