« first day (914 days earlier)      last day (36 days later) » 

11:40 PM
Hello
If $x+y+z=0$, then $$3\bigg(3-\frac{x^2}{yz}\bigg)\bigg(3-\frac{y^2}{zx}\bigg)\bigg(3-\frac{z^2}{xy}\bigg)$$ $$=\bigg(\frac xy\bigg)^3+\bigg(\frac yx\bigg)^3+\bigg(\frac yz\bigg)^3+\bigg(\frac zy\bigg)^3+\bigg(\frac zx\bigg)^3+\bigg(\frac xz\bigg)^3$$ $$+ \;6\bigg(\frac{yz}{x^2}+\frac{zx}{y^2}+\frac{xy}{z^2}\bigg)$$
I think this is true. I believe I have a two-page proof of this. I'm wondering if someone else here wants to attempt to prove this :P
 

« first day (914 days earlier)      last day (36 days later) »