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Let $R$ be an integral domain of characteristic $p\ge 2$, and let $R[x]$ be the ring of polynomials in $x$ with coefficients in $R$.

Which one of the following statements is true?

$(x+a)^p=x^p+a^p$ for all all $a\in R$.

$f(x)=g(x)$ in $R[x]$ if and only if $f(a)=g(a)$ for all $a\in R$.

There is no infinite integral domain with characteristic $p$.

$A[x]$ does not have characteristic $p$