Solve the system congruences x 4 mod 5 x 7 mod 8 x 3 mod

Solve the system congruences x = 4 mod 5 x = 7 mod 8 x = 3 mod 9

Solution

Something is wrong with 3mod9 because its creating problem

for example this isis one goodmoethod

P/7 => remainder 1
P/9 => remainder 2
P/11 => remainder 3

2P/7 => remainder 2
2P/9 => remainder 4
2P/11 => remainder 6

Now comes the tricky part.. Notice that if we add 5 to 2P , these equation will become completely divisible by 7,9 and 11 respectively, i.e. remainder becomes 0.

2P+5/7 => remainder 0
2P+5/9 => remainder 0
2P+5/11 => remainder 0

this means 2P+5 is divisible by 7,9 & 11. So it will be divisible by 7x9x11=693

2P+5=693
2P= 688
P=344