Tessellate S.T.E.M.S - Mathematics - College - Set 3 - Problem 2

Let $R$ be a ring such that $R \cong R \times R$ .

$\textbf{Statement 1.}$ There is an injective ring homomorphism from $\mathbb{Z}$ to $R$ .

$\textbf{Statement 2.}$ There is an injective ring homomorphism from $\mathbb{Z}/p\mathbb{Z}$ to $R$ for some prime $p$ .

Which of the above two statements is/are true?

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This problem is a part of Tessellate S.T.E.M.S.