Dan Drake 🦆I'm absurdly excited to learn that 2024 = 2³+3³+4³+5³+6³+7³+8³+9³.
...and it's because:
2025 = 45², and
45=1+2+⋯+9, and
(1+⋯+𝑛)²=1³+⋯+𝑛³ !
Via https://www.reddit.com/r/math/comments/18tr14a/2024_2³3³4³5³6³7³8³9³/.
Art Smart@ddrake I'll double check it, but before I do, let me note that at the end of your fourth equation, you should remove the exclamation point, as it implies a factorial. I realize you meant it for emphasis, but the factorial makes the equation incorrect.
@ArtSmart ack!
The use of exclamation points in mathematical prose is the bane of my existence, because (1) I'm a combinatorics person, and hence love factorials; (2) am usually pretty excited when I write about math.
So, I am *constantly* in agony about the ambiguity of ending a sentence that contains an equation with an exclamation point.
You could just do periods after factorials, and get things like:
We know that 6 = 3!.
But of course, then if you are excited, you get a similar problem:
We know that 6 = 3!!
(Is that "3 factorial, exclamation point", or 3 double factorial?)
@ddrake I hear you. And yes, 3!! = 6! = 720
Whichever mathematician thought of using the exclamation point for factorials didn't really think it through, I guess. Bummer
Don't forget you can edit your toot to remove the errant exclamation point