MathDB

Let

f(x)

and

g(y)

be two monic polynomials of degree=

n

having complex coefficients. We know that there exist complex numbers

a_i,b_i,c_i \forall 1\le i \le n

, such that f(x)\minus{}g(y)\equal{}\prod_{i\equal{}1}^n{(a_ix\plus{}b_iy\plus{}c_i)}. Prove that there exists

a,b,c\in\mathbb{C}

such that f(x)\equal{}(x\plus{}a)^n\plus{}c\text{ and }g(y)\equal{}(y\plus{}b)^n\plus{}c.

Problem Statement