Timeline for Does there exist a polynomial 𝑃(𝑥,𝑦) which detects all non-squares?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2023 at 1:27 | comment | added | fedja | For 3 variables the theory of Pell's equation is a huge overkill: $(x+y+z-1)^2-(4x+2y-4)$ works just as nicely. | |
| Oct 21, 2022 at 21:43 | answer | added | Pace Nielsen | timeline score: 3 | |
| Oct 21, 2022 at 21:14 | comment | added | Peter Taylor | @IlyaBogdanov, I suspect you are aware of the problem, but the people who upvoted your comment may not be. The same construction would give $Q(x, y) = \frac{-(x+y)^3 + 267(x+y)^2 + 1161(x+y) + 12960x - 7907}{12960}$ but because the spacing of the antidiagonals is no longer consistent we run into the occasional integer value in the gaps, and so it does represent some cubes. | |
| Oct 21, 2022 at 11:19 | comment | added | Peter Taylor | Along similar lines to @IlyaBogdanov's comment, $P(x, y) = \frac{(x+y)^2 + 2(x-y) + 1}4$ detects non-squares, but doesn't meet the requirement of integral coefficients. | |
| Oct 21, 2022 at 7:56 | comment | added | Ilya Bogdanov | Notice that $(x+y-1)(x+y)/2+y$ detects all non-triangular numbers. | |
| S Oct 21, 2022 at 1:06 | review | First questions | |||
| Oct 21, 2022 at 1:26 | |||||
| S Oct 21, 2022 at 1:06 | history | asked | Prism | CC BY-SA 4.0 |