We say that the polynomials f(x) and g(x) are congruent modulo n as polynomials if for each power of x the coefficients of that power in f(x) and g(x) are congruent modulo n. For example, 11x3 + x2 + 2 and x3 − 4x2 + 5x + 22 are congruent as polynomials modulo 5. The notation f(x) ≡ g(x)(mod n) is often used to denote that f(x) and g(x) are congruent as polynomials modulo n. In Exercises, assume that n is a positive integer with n > 1 and that all polynomials have integer coefficients.
Show that if f1(x) and g1(x) are congruent as polynomials modulo n and f2(x) and g2(x) are congruent as polynomials modulo n, then
a) (f1 + f2) and (g1 + g2)(x) are congruent as polynomials modulo n.
b) (f1 f2) and (g1g2)(x) are congruent as polynomials modulo n.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.