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Remember that Diophantine equations accept integer solutions, only.
Write the equation in the slope intercept form.
64y = -15x + 1
Dividingy by 64 both sides => y = -(15/64)*x + 1/64
Notice that the only factor that can divide c (c=1) is 1.
From this point, you have no reason to continue to solve the equation because it will not lead you to integer solutions.
ANSWER: The Diophantine equation has no integer solutions.
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