Hello world :)

[blamocur]

[imath]\forall \;:\;[/imath] Happy [imath]\sqrt{2024^2 + 90^2}[/imath]-th !!

 

[blamocur]

... [imath]= \sqrt{2024^2 + 4\times 2025}[/imath]

 

[fresh_42]

Happy New Year @all from my side, too!

I haven't found any interesting properties of 2026; however, 2026 = 2 * 1013, and 1013 is pretty fancy:

 

[blamocur]

... [imath]= \sqrt{2024^2 + 4\times 2025}[/imath]

just realized that this one is trivial: [imath](n+2)^2 = n^2 + 4(n+1)[/imath]

 

[fresh_42]

just realized that this one is trivial: [imath](n+2)^2 = n^2 + 4(n+1)[/imath]

The funniest equation I ever saw was
[math] 2^n+7^n+8^n+18^n+19^n+24^n=3^n+4^n+12^n+14^n+22^n+23^n \text{ for } n =0,1,...,5 [/math]
But back to 2026:
[math] 2026=(45 +\mathrm{i})\cdot (45 -\mathrm{i}) [/math]