Let \(\mathbb{N}\) = {1, 2, 3, ...} be the set of natural numbers. Which of the following functions from \(\mathbb{N}\) × \(\mathbb{N}\) to \(\mathbb{N}\) are injective?

1
f1(m, n) = 2m 3n
2
f2(m, n) = m2 + m + n
3
f3(m, n) = m3 + n3
4
f4(m, n) = m n3

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