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Consider the equation \(8x + 12y = 2\). Does this equation admit any integer solutions \((x, y)\)?

Yes, because \(8\), \(12\), and \(2\) are all even.
Yes, because \(8 + 12 > 2\).
No, because \(\gcd(8, 12) = 4\) and \(4\) does not divide \(2\).