Thread: Congruence uncertainty

Suppose f(x)and g(x)∈Z_7 [x]. Suppose also that f(x)≡g(x)(mod x). What can we say about f(0)and g(0)?

With this problem i am jus not sure if i am over thinking it because we have done congruences with ideals and in F[x].. would fall under just dealing with F[x]

Originally Posted by empressA88

Suppose f(x)and g(x)∈Z_7 [x]. Suppose also that f(x)≡g(x)(mod x). What can we say about f(0)and g(0)?

With this problem i am jus not sure if i am over thinking it because we have done congruences with ideals and in F[x].. would fall under just dealing with F[x]

f and g are 7 th degree polynomials in in x. Saying that they are congruent "mod x" f- g is a multiple x which, in turn, means f- g has no constant term.

is that f - g, or are you say f and g?

Originally Posted by HallsofIvy

f and g are 7 th degree polynomials in in x. Saying that they are congruent "mod x" f- g is a multiple x which, in turn, means f- g has no constant term.

Doesn't mean and are polynomials with coefficients in ?

If so then the constant term of .

But this constant term is equal to . Therefore .