Quadratic Residue (Part-2) Definition of Quadratic Residue

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In this video, I have given the definition of Quadratic Residue.
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Excellent instructional video. Thank you.

IODell
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could you elucidate the book's part (by burton) when it refers to consecutive pairs of that modulo 13 (3&4 and 9&10 being the instances, 3²4² ≡ 9²10² ≡ 1 (mod13)).
So that there are ¼(p–4–(-1)^(½(p-1))) consecutive pairs that satisfy the congruence

spiderjerusalem
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Could please clarify how to determine whether a quadratic residue is quadratic non - quadratic towards the end of the video?

gunanesansingarajah
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Why did u take the values of x from 1 to 12 ?(I agree a can range from 0 to 12 since a is the remainder but there is no limitation on x)

burugupallykaushik