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Criteria for Solvability of Certain Congruences

Published online by Cambridge University Press:  20 November 2018

Joseph B. Muskat
Joseph B. Muskat*
Affiliation:
University of Pittsburgh
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Lower case italics will denote rational integers, while lower case Greek letters will denote algebraic integers. The Law of Quadratic Reciprocity can be formulated as follows:

If p and a are distinct odd primes, then a is a quadratic residue (mod p) if and only if ( — 1)(p-1)/2p is a quadratic residue (mod q).

Let Xp denote the non-principal quadratic character (mod p) and let ζp be a primitive pth. root of unity. Then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 343 - 352
Copyright
Copyright © Canadian Mathematical Society 1964

References

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