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Forum: Number Theory Discussion Group 2020-11-02, 20:28
Replies: 12
Views: 3,453
Posted By bhelmes
alpha=arctan (1/11)=5,194428908 sin...

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
Forum: Number Theory Discussion Group 2020-11-02, 18:40
Replies: 12
Views: 3,453
Posted By bhelmes
For mathematical curosity and practical use: ...

For mathematical curosity and practical use:


Is it possible to calculate the square root of a quadratic residium by using the tangens function ?


I have the pythagoraic tripple 11,60,61...
Forum: Number Theory Discussion Group 2020-11-01, 20:00
Replies: 12
Views: 3,453
Posted By bhelmes
How do you calculate the mapping function ? ...

How do you calculate the mapping function ?


Thanks for your clear explications.
Forum: Number Theory Discussion Group 2020-11-01, 09:25
Replies: 12
Views: 3,453
Posted By bhelmes
??? I think 61 is a prime ideal in the Gaussian...

???
I think 61 is a prime ideal in the Gaussian integers,
61=(6+5i)(6-5i)



http://devalco.de/poly_xx+yy_demo.php?radius_a=11&radius_b=60&radius_c=61


I understand that -i²=1
Forum: Number Theory Discussion Group 2020-10-31, 18:57
Replies: 12
Views: 3,453
Posted By bhelmes
(16+29i)²=(25+13i) mod 61 (25+13i) can be...

(16+29i)²=(25+13i) mod 61
(25+13i) can be mirrored at the main diagonale,
so that the point of the unit circle (13+25i) "=" (25+13i)


tan (alpha)=3/4, tan (alpha/2)=(5-4)/3=1/3 if this helps
...
Forum: Number Theory Discussion Group 2020-10-31, 03:35
Replies: 12
Views: 3,453
Posted By bhelmes
calculation of the non quadratic residium

A peaceful and pleasant night for you,


I know that from the pyth. trippel (3, 4, 5) - > 3/5, 4/5 mod 61 = (13+25i)

1. and that (13+25i)^30 = 1 mod 61
2. and |16+29i| = (16²+29²) =...
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