I'm stuck with the following equation:
$$x^3 + a \cdot x^2 + b \cdot x + c = d $$ $$ x, a, b, c, d > 1,$$ $$ x < d $$ $$ a < d $$ $$ b < d $$ $$ c < d $$
$$ x, a, b, c, d \in \Bbb{Z} $$
We need to proof that this equation hasn't got any integers solutions for $x$.
Tried several times, but didn't find any approach. Will be happy for hints.