Timeline for Does there exist a polynomial 𝑃(𝑥,𝑦) which detects all non-squares?
Current License: CC BY-SA 4.0
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| Oct 21, 2022 at 22:22 | comment | added | Peter Taylor | A direct approach along these lines would be to target $(x^2 + y)[1 \le y \le 2x]$ as $(x^2 + y)[1 \le y,z][y+z = 2x + 1]$ giving $$E(x,y,z) = (x^2 + y)(1 - (2x-y-z+1)^2)$$ I'm not sure that it makes it easier to eliminate the third variable, though. | |
| Oct 21, 2022 at 21:48 | comment | added | Peter Taylor | It should be noted that the almost-answer I proposed in comments evaluates to non-integers when $x+y$ is even, so removing the fractional component could cause new problems. | |
| Oct 21, 2022 at 21:43 | history | answered | Pace Nielsen | CC BY-SA 4.0 |