Question

The value of the Legendre symbol (-461/383) is:
a) -1
b) 1
C) 0
d) None of the above
​

Answer 1

Answer:

-1 is the answer of the question so the correct answer is option a.

Answer 2

The Legendre symbol of (-461/383) is 1

Given:

The fraction of  (-461/383)

To Find:

The Legendre symbol of the fraction   (-461/383)

Solution:

The Legendre symbol can be calculated  using the table,

To get the value ,

Use the Legendre symbol,

= $\frac{a}{p}$

Legendre symbol = -461/383

= $\frac{-39}{383}$

= $\frac{32}{-39}$

= $\frac{16}{-39}$

Legendre symbol = $\frac{16}{-39}$

Legendre symbol = $\frac{8}{-39}$

Legendre symbol = $\frac{4}{-39}$

Legendre symbol = $\frac{2}{-39}$

Legendre symbol = $\frac{1}{-39}$

Legendre symbol = 1

The value of the Legendre symbol (-461/383) = 1

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