Question 102
let $f(x) = bx^2 + cx + a$, $g(x) = cx^2 + ax + b$, where $a, b, c$ are integers. given that $f(1234) = g(1234)$, determine whether the equality $f(1) = 2009$ can hold. The integers of $a, b, c$ are such that the values of the square trinomials of $bx^2 + cx + a$ and $cx^2 + ax + b$ at $x = 1234$ are the same. Can the first trinomial at $x = 1$ take the value of 2009?