6. (i) (ii) State the law of quadratic reciprocity. Compute the Legendre symbol 409 Show that the Diophantine equation y² = 13x³ - 3 has no solutions, i.e., no pair of integers (x, y) satisfies this equation. (iii)

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6. (i)
(ii)
State the law of quadratic reciprocity.
Compute the Legendre symbol
211
(2009).
Show that the Diophantine equation
y² = 13x³ - 3
has no solutions, i.e., no pair of integers (x, y) satisfies this equation.
(iii)
Transcribed Image Text:6. (i) (ii) State the law of quadratic reciprocity. Compute the Legendre symbol 211 (2009). Show that the Diophantine equation y² = 13x³ - 3 has no solutions, i.e., no pair of integers (x, y) satisfies this equation. (iii)
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