Z पूर्णांकों का समूह है, समूह बनाता है यदि ∗ है:

1
∗(a, b) = a  + b + 2
2
∗(a, b) = 2a + b
3
∗(a, b) = (a + b)/2
4
∗(a, b) = a2 + b

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