489 reputation
129
bio website
location
age
visits member for 1 year, 11 months
seen Apr 9 at 10:22

Apr
2
revised Miller-Rabin primality test and testing one
added 1 characters in body
Apr
2
asked Miller-Rabin primality test and testing one
Apr
2
comment Taking the modulus of the power?
@DanielFischer - I see, thank you :)
Apr
2
asked Taking the modulus of the power?
Mar
31
awarded  Famous Question
Mar
20
accepted Finding a parameter for two solutions in a field
Mar
19
comment Finding a parameter for two solutions in a field
@JohnHabert - Mhm, I see. Thank you a lot again :)
Mar
19
comment Finding a parameter for two solutions in a field
@JohnHabert - thank you, that's a great fast way. However, this won't necessarily work for other problems like this, right? I mean - say we have $3x^2 +5x +m=0$, also in $Z_{13}$. Then, we have $\Delta = 12-12m \equiv m-1$ and we can't use such shortcut. That's why I'm curious about a general faster way than brute forcing to find a square root, not just for this specific example.
Mar
19
comment Finding a parameter for two solutions in a field
@JohnHabert - no, regretfully I haven't... But now after looking at it for a while - how does this help here?
Mar
19
asked Finding a parameter for two solutions in a field
Mar
19
comment Two different delta values in a quadratic equation
That's exactly what I didn't get, thank you a lot! :)
Mar
19
accepted Two different delta values in a quadratic equation
Mar
19
comment Two different delta values in a quadratic equation
@JohnHabert - oh, ok. In the example above, I end up with the same solutions (2/10 which is not in $Z_{11}$ and 1 which is) whichever delta value I choose. Does that mean I can always choose either one in such case?
Mar
19
comment Two different delta values in a quadratic equation
@JohnHabert - Yes, but also $4 \equiv -7 (\mod 11)$ so which one do I use if I want to just find the solutions using the regular $\frac{-b +- \sqrt{\Delta}}{2a}$?
Mar
19
asked Two different delta values in a quadratic equation
Mar
19
comment Finding solutions belonging to given field
@JyrkiLahtonen - I see, thank you. One last question: is there a way to do it other than brute force? In the $Z_7$ case, what I wrote above is true but it was only my guess and I wasn't sure of it until I made Wolfram check if there is no $k$ such that $k^2 \equiv 5 (\mod 7)$ and I guess such guesses won't be treated too nicely on the test. Is there a better way or I'd just have to prove that there is no such k in some fancy way on the test?
Mar
19
comment Finding solutions belonging to given field
@JyrkiLahtonen - Thank you. But in a case like $Z_7$, there is no square root of five, right? It'd have to be some $k^2 \equiv 5 (\mod 7)$ but then we'd need $7r+5$ being a square of some integer and there is none. Does this mean there are no solutions to the $Z_7$ case?
Mar
19
asked Finding solutions belonging to given field
Mar
6
awarded  Critic
Mar
5
comment Proving equality with floor by contradiction
@KarolisJuodelÄ— - right, a naive mistake on my side. Thank you very much :)