Question

Hiw we find inverse value in chinese remainder theorem

Answer 1

 need to solve the system of equations:

x≡13mod11x≡13mod11

3x≡12mod103x≡12mod10

2x≡10mod6.2x≡10mod6.

So I have reduced this to

x≡2mod11x≡2mod11

x≡4mod10x≡4mod10

x≡2mod3x≡2mod3

so now I can use CRT. So to do that, I have done

x≡{2×(30−1mod11)×30+4×(33−1mod10)×33+2×(110−1mod3)×110}mod330x≡{2×(30−1mod11)×30+4×(33−1mod10)×33+2×(110−1mod3)×110}mod330

={2(8−1mod11)⋅30+4(3−1mod10)⋅33+2(2−1mod3)⋅110}mod330={2(8−1mod11)⋅30+4(3−1mod10)⋅33+2(2−1mod3)⋅110}mod330