286 = 2 x 11 x 13.
286 is the 11th tetrahedral number.
286 is a heptagonal number.
286 is the number of rooted trees with 9 vertices.
286 is 2121 in base 5 and 141 in base 15.
286 is the shorthand for the Intel 80286 microprocessor chip.
286 is the shorthand for the Intel 80286 microprocessor chip.
Some analytical properties of the number 286
ReplyDelete1) 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