Question

Find all solutions to the following Diophantine equations:

(a) x² = y³ .
(b) x² −x = y³.
(c) x² = y⁴ −77
(d) x³= 4y² +4y−3.

Answer 1

The solutions to the given Diophantine equations are (a) x = 2, y = 2; (b) x = 1, y = 3; (c) x = 400, y = 2101; (d) x = 1, y = 2.

Step-by-step explanation:

Diophantine equation (a): x² = y³

Solutions: x = 2, y = 2

Diophantine equation (b): x² −x = y³

Solutions: x = 1, y = 3

Diophantine equation (c): x² = y⁴ - 77

Solutions: x = 400, y = 2101

Diophantine equation (d): x³ = 4y² + 4y - 3

Solutions: x = 1, y = 2