[SOLVED] Polynomial of degree 4 (mod 5) reduction

[Aya2002]

Hello friends,

Today I have faced a simple problem. It is the following polynomial of degree 4 (mod 5):

g(x) = x + 2x^4

how it will be (3 + 2x^2)(1+x^2)+(2+x) mod 5 ?

help please.
regards

 

[trav1s]

Just clarification,
you are asking to prove that
x + 2x^4 = mod5[(3 + 2x^2)(1+x^2)+(2+x)] ?

 

[Aya2002]

Just clarification,
you are asking to prove that
x + 2x^4 = mod5[(3 + 2x^2)(1+x^2)+(2+x)] ?

yes friend, this is exactly what I need.

Thanks

 

[albbg]

Developing the polynomial you will obtain:

2*x^4 + 5*x^2 + x + 5 = 2*x^4 + x + 5*(x^2 + 1)

rember that sum of moduli is equal to the modulus of the sum, then

mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] + mod5[5*(x^2 + 1)]

but the last term is always zero since the remainder of 5*(x^2 + 1)/5 is zero then:

mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ]

 

[Aya2002]

Developing the polynomial you will obtain:

2*x^4 + 5*x^2 + x + 5 = 2*x^4 + x + 5*(x^2 + 1)

rember that sum of moduli is equal to the modulus of the sum, then

mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] + mod5[5*(x^2 + 1)]

but the last term is always zero since the remainder of 5*(x^2 + 1)/5 is zero then:

mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ]

my friend,
I mean how to reduce g(x) to (3 + 2x^2)(1+x^2)+(2+x) mod 5

I know how to develop it, but I need to reduce it to the above equation (mod 5).

regards