Timeline for Cubic function $\mathbb{Z}^2 \to \mathbb{Z}$ cannot be injective

7 events

when toggle format	what		by	license	comment
May 22, 2021 at 8:34	history	edited	Greg Egan	CC BY-SA 4.0	Noted simple construction for quadratic
May 11, 2021 at 11:55	history	edited	Greg Egan	CC BY-SA 4.0	Mentioned explicit formulas for the tangent line construction
May 11, 2021 at 0:42	history	edited	Greg Egan	CC BY-SA 4.0	Added example of repeated-value points not on a tangent line
May 9, 2021 at 6:57	history	edited	YCor		edited tags
May 9, 2021 at 1:13	comment	added	user44143		By contrast, the quartic $(3x^2+x+1)+(3x^2+x+1+3y^2+y+1)^2$ is injective on $\mathbb{Z}^2$. This comes from 10.3 at zacharyabel.com/papers/Favorite-Problem_A07_HCMR.pdf, as linked in the answer at mathoverflow.net/questions/138106/…
May 9, 2021 at 0:19	history	edited	Greg Egan	CC BY-SA 4.0	Fixed typo
May 9, 2021 at 0:10	history	asked	Greg Egan	CC BY-SA 4.0