Question

Using CRT solve x≡1(mod3),x≡2(mod3),x≡3(mod3) *

Answer 1

Answer:

n1=3, n2=3, n3=3

N = n1n2n3 = 3 x 3x 3 = 27

c1=1, c2=2, c3=3.

N1 = N/n1 = 9; d1 = 9-1 (mod 3) = 0 [check: 0*9=0≡0(mod 3)]

N2 = N/n2 = 9; d2 = 9-1 (mod 3) =0 [check: 0x9=0≡0 (mod 3)]

N3 = N/n3 = 9; d3 = 9-1 (mod 3) = 0 [check: 0x9=0≡0 (mod 3)]

x ≡ c1N1d1 + c2N2d2 + c3N3d3 (mod N)

x = (1x27x0) + (2x27x0) +(3x27x0) = 0≡ 0