Integer polynomial

Algebra Level 5

Consider all polynomials with integral coefficients

anxn+an1xn1++a1x+a0=0, a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}=0,

such that 43\frac{4}{3} is one of its roots, 3a0,3 | a_0, and 4an4 | a_n.

Over all such polynomials, find the smallest positive value of an+a0 a_n + a_0 .

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