contestada

Factor x^2 -3x-3 in F5(x) p=5
it says -3 =2(mod5)-----------how did they come up with this
x^2-3x-3 = x^2 -3x +2--------how did they come up with this

Respuesta :

LammettHash
[tex]-3=2-5\implies -3\mod5=2\mod5[/tex]

When taking a polynomial modulo [tex]n[/tex], you reduce its terms' coefficients modulo [tex]n[/tex], so that, in conjunction with the result above,

[tex]x^2-3x-3\equiv x^2-3x+2\mod5[/tex]

For completeness, the linear term's coefficient should also get reduced in the same way as the constant term, so that

[tex]x^2-3x-3\equiv x^2+2x+2\mod5[/tex]