20201102, 20:28  #12 
Mar 2016
3×5^{3} Posts 
alpha=arctan (1/11)=5,194428908 sin (alpha)=0,090535746 61²*sin (alpha)=336,883511024 337 =32 mod 61 = 29 mod 61 cos (alpha)=0,995893206 61²*cos (alpha)= 3705,718621265 3705 = 45 = 16 mod 61 29² + 16² = 1 mod 61 (o.k.) 29²  (16i)² = i² (29i)² +16² = 1 is this o.k. ? 
20201103, 13:58  #13  
Feb 2017
Nowhere
2×3×7×127 Posts 
Quote:
For primes p congruent to 1 (mod 4) I don't know of any faster way than factoring x^{2}  r over the finite field with p elements. In PariGP sqrt(Mod(r, p)) will return the square root in (0,p/2) if p is prime and r is a quadratic residue (mod p). 

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