Question-41066

Question Number 41066 by Tawa1 last updated on 01/Aug/18

Answered by candre last updated on 03/Aug/18

x \equiv 1 (\mod 3)

x \equiv 3 (\mod 5)

x \equiv 3 (\mod 7)

b y c h i n e s e r e m a i n d e r t h e o r e m

5 \cdot 7 x_{1} \equiv 1 (\mod 3)

2 x_{1} \equiv 1 (\mod 3)

x_{1} \equiv 2 (\mod 3)

3 \cdot 7 x_{2} \equiv 1 (\mod 5)

3 \cdot 2 x_{2} \equiv 1 (\mod 5)

6 x_{2} \equiv 1 (\mod 5)

x_{2} \equiv 1 (\mod 5)

3 \cdot 5 x_{3} \equiv 1 (\mod 7)

15 x_{3} \equiv 1 (\mod 7)

x_{3} \equiv 1 (\mod 7)

x \equiv 1 \times 5 \times 7 \times 2 + 3 \times 3 \times 7 \times 1 + 3 \times 3 \times 5 \times 1 (\mod 3 \times 5 \times 7)

x \equiv 70 + 63 + 45 (\mod 105)

x \equiv 178 (\mod 105)

x \equiv 73 (\mod 105)

Commented by Tawa1 last updated on 03/Aug/18

God bless you sir

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