Quadratic Reciprocity Examples — Number Theory 24

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Комментарии
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Nice proofs. Quadratic residues and Quadratic Reciprocity are subjects that require some practice to really gain an intuition, so this video will probably be really helpful.

JM-usfr
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I'm confused: at 5:25, I think the wrong rule is appealed to. to evaluate (2 / 11), the rules for (-2 / p) apply, rather than the rules for (-1 / p), no?

musiclover
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‏‪4:39‬‏
professor penn didn't proof the rule that we can use p/q instead of using q/p with a minus sign or not

conanedojawa
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On the theorem proof, we should also consider the case where N itself is prime, therefore does not admit any prime factor. But then, we showed that N is 3 mod 8. Therefore N itself is a new prime of the form 3 mod 8, that doesn't equate to any of the finite set of pi. This contradict the initial assumption of this set being finite.

AbuMaxime