Solve-the-system-of-congruences-x-2-mod-3-x-5-mod-7-

Question Number 80504 by Rio Michael last updated on 03/Feb/20

Solve the system of congruences

x \equiv 2 (\mod 3)

x \equiv 5 (\mod 7)

Commented by mr W last updated on 03/Feb/20

x = 21 n + 5

Commented by Rio Michael last updated on 03/Feb/20

p l e a s e c h e c k t h i s s i r :

x \equiv 2 (m o d 3) \Rightarrow x = 3 k + 2

3 k + 2 \equiv 5 (m o d 7) \Rightarrow 3 k \equiv 3 (m o d 7) k h a s n o

s o l u t i o n h e r e s i r!

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

R_{1} = 7 a n d R_{2} = 3

7 X_{1} \equiv 1 (m o d 3) \Rightarrow X_{1} \equiv 1 (m o d 3)

3 X_{2} \equiv 1 (m o d 7) \Rightarrow X_{2} \equiv 5 (m o d 7)

x \equiv R_{1} a_{1} X_{1} + R_{2} a_{2} X_{2} (m o d n_{1} n_{2})

x \equiv (7) (2) (1) + (3) (5) (5) (m o d 21)

x \equiv 5 (m o d 21)