Ex. 1. Find all integer solutions to the following Diophantine equation: x3 + 3 = 4y2 + 4y.
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Answer:
x³ + 3x = 4y² + 4y
• Taking x common in first equation and 4y in second equation.
= x (x² + 3) = 4y (y + 1)
= (x - 4) (x²+ 3 -y - 1)
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