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Anglický jazyk
Quadratic Reciprocity
Autor: Lambert M. Surhone
High Quality Content by WIKIPEDIA articles! The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which gives conditions for the solvability of quadratic equations modulo prime numbers. There are a number of equivalent... Viac o knihe
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O knihe
High Quality Content by WIKIPEDIA articles! The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which gives conditions for the solvability of quadratic equations modulo prime numbers. There are a number of equivalent statements of the theorem, which consists of two 'supplements' and the reciprocity law: Let p, q 2 be two distinct (positive odd) prime numbers. Then (Supplement 1) x2 = -1 (mod p) is solvable if and only if p = 1 (mod 4). (Supplement 2) x2 = 2 (mod p) is solvable if and only if p = ±1 (mod 8). (Quadratic reciprocity) Let q * = ±q where the sign is plus if q = 1 (mod 4) and minus if q = -1 (mod 4). (I.e. |q *| = q and q * = 1 (mod 4).) Then x2 = p (mod q) is solvable if and only if x2 = q * (mod p) is solvable.
- Vydavateľstvo: OmniScriptum
- Rok vydania: 2026
- Formát: Paperback
- Rozmer: 220 x 150 mm
- Jazyk: Anglický jazyk
- ISBN: 9786130346034
