Timeline for What is the shortest polynomial divisible by $(x-1)(y-1)(x^2y-1)$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2017 at 19:33 | comment | added | YCor | @JoeSilverman oops thanks, I misread "lower bound" to "upper bound". | |
| Jun 27, 2017 at 18:46 | comment | added | Joe Silverman | @PeterMueller You should post your answer as an Answer, rather than a Comment. Although the OP didn't ask for the solution of smallest total degree, I think it is worth having such a solution. | |
| Jun 27, 2017 at 18:41 | comment | added | j.c. | @PeterMueller In fact, Fedor Petrov's example is equal to $-(x^4y^2+x^2y^2+x^2y+y^2+y+1)g$ where $g$ is your polynomial. | |
| Jun 27, 2017 at 18:11 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
added 166 characters in body
|
| Jun 27, 2017 at 16:32 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
added 103 characters in body
|
| Jun 27, 2017 at 16:20 | comment | added | Joe Silverman | @YCor The OP indicated why 6 is optimal. So all that's required is to perform the division to see that the quotient is a polynomial. (Which admittedly is best done using one's computer package of choice.) I agree that it would be nice if Fedor Petrov gave some indication of how he found this solution, but one might equally well say that with the solution in hand, it makes a nice exercise to figure out how one might find it. | |
| Jun 27, 2017 at 15:56 | history | answered | Fedor Petrov | CC BY-SA 3.0 |