Solution:

2x==3==48 mod45

x==24

The property of congruence formula is used here: when both sides of the equal sign are divided by the number of modular coprime, the congruence formula is still valid.

2. Solve the congruence group:

X= 1 (modulo 2)

x=2(mod5)

X=3 (modulus 1 1)

Solution:

x = = 1 = = 5 * 1 1 mod 2

x==2==2** 1 1 mod 5

x = = 3 = = 2 * 5 *(3)mod 1 1

[

Note: The content in brackets here is to illustrate the principle of China's remainder theorem (Sun Tzu's theorem), so it is unnecessary to write it when solving it formally.

In fact, as can be seen from the following process, China's remainder theorem can be applied flexibly and simplified.

It is obvious that:

x = = 1 = = 5 * 1 1+2 * * 1 1+2 * 5 *(3)mod 2

x = = 2 = = 5 * 1 1+2 * * 1 1+2 * 5 *(3)mod 5

x = = 3 = = 5 * 1 1+2 * * 1 1+2 * 5 *(3)mod 1 1

]

So the solution is:

x = = 5 * 1 1+2 * * 1 1+2 * 5 *(3)mod 2 * 5 * 1 1

x==47 mod 1 10