| 释义 |
congruence equation An equation involving congruences. As division is not always well defined in modulo n arithmetic, not all standard algebraic operations apply; for example, the congruence congruence ax ≡ b (mod n) has a unique solution in ℤn if and only if a and n are coprime. Also x2−1 ≡ 0 (mod 8) is a quadratic equation with four solutions x ≡ 1, 3, 5, or 7 (mod 8), factorizable in two different ways: x2−1 ≡ (x − 1)(x + 1) ≡ (x − 3)(x − 5). When the modulus n is prime, ℤn is a field and these issues do not arise. See also Chinese Remainder Theorem.
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