[Edit this paragraph] The concept of fractional modular congruence was given by the mathematical prince Gauss (Germany). Two integers A and B, if the remainder obtained by dividing them by the integer M is equal, are said to be congruent with the module M and recorded as a ≡ b (mod m).

Read congruence in b module m

Many people must know the mod problem of integers. But sometimes we also encounter the mod problem of scores.

For example:

1/2 mod 7 = 4；

1/3 mod 7 = 5；

1/4 mod 7 = 2；

1/5 mod 7 = 3；

1/6 mod 7 = 6；

1/7 mod 7 software will display: "Error, modulus inversion does not exist", that is, there is no output.

And we also found that: 2 * 4mod7 =1; 3 * 5 mod 7 = 1； 4 * 2 mod 7 = 1； 5 * 3 mod 7 = 1； 6 * 6 mod 7 = 1；

However, we can't find an integer m that makes 7 * m mod 7 =1; That's why we say "error, modular inversion does not exist".

For integers m, n, (m

Step (1): Find an integer p so that 1/m +p=( 1+p*m)/m, so that this integer (1+p*m) is a multiple of n, that is, (1+).

(2): The problem is transformed into 1/m ≡ -p mod n, and only the value of -p mod n needs to be obtained.

Example:

1/3 mod 7=？ ; 1/3+2=7/3; -2 mod 7=5, which means1/3mod7 = 5;