Question 141
Given a quadratic trinomial $p(x)$ with integer coefficients such that $p(x)$ is not divisible by $3$ for all integers $x$.
Prove that there exist polynomials $f(x)$ and $h(x)$ with integer coefficients such that
$$
p(x) \cdot f(x) + 3h(x) = x^6 + x^4 + x^2 + 1.
$$
Prove that there exist polynomials $f(x)$ and $h(x)$ with integer coefficients such that
$$
p(x) \cdot f(x) + 3h(x) = x^6 + x^4 + x^2 + 1.
$$