这是解线性同余。

回答: 又有数学题求解，先谢谢了！ 由 琼岛春荫 于 2012-04-22 21:04:14

Theorem:

The linear congruence ax = b (mod n) has a solution if and only if d | b, where d = gcd (a,n). If d | b, then it has d mutually incongruent solutions modulo n.

3x = 1 (mod 11) has only one solution since gcd(3,11) = 1 which is x = 4 (mod 11);

20x = 52 (mod 7)  => 20x = 3 (mod 7) has only one solution since gcd (20, 7) =1 which is x = 4 (mod 7);

20 x = 52 (mod 88) has four solutions since gcd (20, 88) = 4 which are:

x = 7, 29, 51, 73 (mod 88).