Timeline for Are the number of solutions to $ax^2+bxy+cy^2\equiv u\pmod{p}$, $(x,y)\in\{0,\dotsc,p-1\}$, the same for all units $u$?
Current License: CC BY-SA 4.0
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| Jun 20, 2022 at 11:39 | comment | added | Joe Silverman | @user47804 First, if you're going to refer people to another MO question, include it as a link. Second, Keith Conrad explained in his comment to your other question that proving that $N(p^n)=p^{n-1}N(p)$ can be done using Hensel's lemma, since in your case the your algebraic variety is smooth (i.e., non-singular) mod $p$. | |
| Jun 20, 2022 at 0:06 | comment | added | user47804 | I have a followup question - #425072 - that might be of interest. | |
| Jun 17, 2022 at 20:01 | history | edited | Joe Silverman | CC BY-SA 4.0 |
Fixed typo
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| Jun 16, 2022 at 22:06 | history | answered | Joe Silverman | CC BY-SA 4.0 |