Some analytical properties of the number 286 1) K=Q quadratic field (+-d)^(1/2 -Quadratic forms over quadratic imaginary field (N is the norm or conjugate) N(3+(-277)^(1/2)=3^2+277*1^2=286 ->z^2-6z+286=0.==> Z=3+-(277)^(1/2)i N(15+(-61)^(1/2)=15^2+61*1^2=286 ->z^2-30z+286=0.==> z=15+-(61)^(1/ 2)i -Quadratic forms over realquadratic field: N(17+(3)^(1/2)=17^2-3*1^2=286 ->z^2-34z+286=0.==> z=17+-(3)^(1/2) N(27+(443)^(1/2)=27^2-443*1^2=286 ->z^2-54Z+286=0. ==> z=27+-(443)^(1/2) http://hojamat.es/parra/cuadrbin.pdf 2) Multiplicative group Let 17*19=323 in which a group is the 286. gcd(286.323)=1 286=14(mód.17)->286=1(mód.19), where gcd (17.19)=1=17(9)+19(-8) If 17(9)(mod 323)=153 and 19(-8)* 14(mod 323)=133, then 286=17(9)*1 +19(-8)*14(mod 323) -> 153+133=286 and therefore f(286)=f(153)+f(133) http://hojamat.es/parra/funesp.pdf

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Some analytical properties of the number 286

1) K=Q quadratic field (+-d)^(1/2

-Quadratic forms over quadratic imaginary field (N is the norm or conjugate)

N(3+(-277)^(1/2)=3^2+277*1^2=286

->z^2-6z+286=0.==> Z=3+-(277)^(1/2)i

N(15+(-61)^(1/2)=15^2+61*1^2=286

->z^2-30z+286=0.==> z=15+-(61)^(1/ 2)i

-Quadratic forms over realquadratic field:

N(17+(3)^(1/2)=17^2-3*1^2=286

->z^2-34z+286=0.==> z=17+-(3)^(1/2)

N(27+(443)^(1/2)=27^2-443*1^2=286

->z^2-54Z+286=0. ==> z=27+-(443)^(1/2)

http://hojamat.es/parra/cuadrbin.pdf

2) Multiplicative group

Let 17*19=323 in which a group is the 286. gcd(286.323)=1

286=14(mód.17)->286=1(mód.19), where gcd (17.19)=1=17(9)+19(-8) If 17(9)(mod 323)=153 and 19(-8)* 14(mod 323)=133, then 286=17(9)*1 +19(-8)*14(mod 323) -> 153+133=286 and therefore f(286)=f(153)+f(133)

http://hojamat.es/parra/funesp.pdf

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