Calculate all the solutions that are created at the same time by the X-4 (mod 5) and X-5 (mod 11) Enable equations.

Introduction to algorithms exercise 31.5-1

According to the remainder theorem of China,

N = 55

A1 = 4,N1 = 5,M1 = 11,11-1 limit 1 (mod 5)

A2 = 5,N2 = 11,M2 = 5, 5-1 running 9 (mod 11)

C1 = 11 (1 mod 5) = 11

C2 = 5 (9 mod 11) = 45

 

A	Bytes	4. 11 + 5. 45	(Mod 55)
	Bytes	44 + 225	(Mod 55)
	Bytes	49	(Mod 55 ).

 

Therefore, all the solutions that make the equation come true at the same time are integers in the form of 49 + 55 K (K is an arbitrary integer.