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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)

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)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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