Question

Evaluate the following Legendre Symbols:

\bigl(\begin{smallmatrix} 139\\ 431 \end{smallmatrix}\bigr)                \bigl(\begin{smallmatrix} 149\\ 439 \end{smallmatrix}\bigr)

30 Nov 2023
Answer :
Word Count : 148

To evaluate the Legendre symbols \(\left(\frac{139}{431}\right)\) and \(\left(\frac{149}{439}\right)\), we use the law of quadratic reciprocity, which states that for prime numbers \(p\) and \(q\) where \(p\) and \(q\) are ______ _______ ________ _________ ________ _________ __________.
__________ _______ _______ ___ ___ _____ _____ _____ _____ ________ ___ _____.
_______ ________ ____ ____ _______ ______.
___ _______ _________ ____ _________ ______ ____ _______ ________ ______ _____ __________.
_________ _________ ______ ____ __________ ________ _______ ___.
________ ___ _____ __________ ________ ___ __________.
_________ ____ __________ _____ ____ ______ ___ ___ _________ __________.
_____ ______ __________ ___ ____ ___ _______ __________.
____ _________ ________ _____ _____ ________.
__________ ___ ______ ______ ______ ______ _____ _________ _________ _________.
_______ ____ _____ _________ _________ __________ _______.
____ ________ _____ _______ ________ _____ _______ ________ _________ _________ ___.
_______ _________ ________ _________ ______ ________ ___ _____ _______.
____ _______ ________ ___ ______ _________.
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