Discussion
The linear diophantine equation \(7x - 8y = 5\) has :
Answer: C
The equation has infinitely many integer solutions, with any two values of \(x\) differing by a multiple of 8.
\(\gcd(7, 8) = 1\) divides 5, so solutions exist. One solution is \(x = 3, y = 2\), since \(21 - 16 = 5\). The general solution is
\[ x = 3 + 8t, \quad y = 2 + 7t, \quad t \in \mathbf{Z} \]
So there are infinitely many solutions, and the \(x\)-values differ by multiples of 8 (the coefficient of \(y\) divided by the gcd). It is the \(y\)-values that differ by multiples of 7, which is the trap in option D.
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