Let $f(x)=x^3+7x^2+9x+10$. Find the value of $p$ such that for every integer $a,b$, the statement
\[
f(a) \equiv f(b) \ (\text{mod } p) \Rightarrow a \equiv b \ (\text{mod } p)
\]
is satisfied.

Let's think step by step and output the final answer within \boxed{}.
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