Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1303-4603-4 |
Объём: | 88 страниц |
Масса: | 153 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
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.
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