If both ab and \(a+b\) are even, then both a and b are even. If \(a, b \in \mathbb{Z}\) and a and b have the same parity, then \(3a+7\) and \(7b-4\) do not. If \(a, b \in \mathbb{Z}\), then \((a+b)^{3...If both ab and \(a+b\) are even, then both a and b are even. If \(a, b \in \mathbb{Z}\) and a and b have the same parity, then \(3a+7\) and \(7b-4\) do not. If \(a, b \in \mathbb{Z}\), then \((a+b)^{3} \equiv a^3+b^3 \pmod{3}\). If \(a \equiv b \pmod{n}\) and \(a \equiv c \pmod{n}\), then \(c \equiv b \pmod{n}\). If \(a \in \mathbb{Z}\) and \(a \equiv 1 \pmod{5}\), then \(a^2 \equiv 1 \pmod{5}\). If a ≡ b (mod n), then a and b have the same remainder when divided by n
