View Single Post
Old 2021-07-31, 15:19   #21
RomanM
 
Jun 2021

31 Posts
Default

Quote:
Originally Posted by Batalov View Post
Refrigerator can easily do 'Grmmmmmmmmmm' and not work actually.
Of course! And quiet too on Peltier elements) This joke mainly about our understanding of life consciousness
Quote:
Originally Posted by Dr Sardonicus View Post
Do you mean b^n - a?
No. Talk was about quadratric case; yes for higher orders.
Quote:
Originally Posted by RomanM View Post
***
Take some integer u>sqrt(p), b=mod(u^2,p); a=mod(b^2,p)=mod(u^4,p);

[From (b-y)^2==0 mod p
b^2-2*b*y+y^2==0 mod p or a-2*b*y+y^2==0;
Solution: y=b-sqrt(b^2-a) (and y=b+sqrt(b^2-a), using first)
Make y an integer, and compute t= b-y =ceil(sqrt(b^2-a))]
***
(b-y)^3=b^3-3*b^2*y+3*b*y^2-y^3
if b<sqrt(p) and b^3>p, a=mod(b^3,p)
one roots (of 3)
((-b)^3+a)^(1/3)+b
(b-y)^4
root
(b^4-a)^(1/4)+b
and so on. Other roots also have importance

Last fiddled with by RomanM on 2021-07-31 at 15:23
RomanM is offline   Reply With Quote