Find all integer x that satisfy a 9x 3 mod 12 b 8x 1 mod 27

Find all integer x that satisfy (a) 9x 3 (mod 12) (b) 8x 1 (mod 27) (c) 6x 8 (mod 380)

Solution

(1) a b mod(m) if m|a-b

Therefore, x={3,7,11,.....} ; x=4n-1 n=1,2,3,......

(2)

Now,next values of x will be,17+27,17+27+27,...

hence, x=27n-10 n=1,2,3,....

(3)

So,the next numbers will be 128+190,128+190+190,...

hence, x=190n-62 n=1,2,3

x	9x-3	DIVIDED BY 12
0	-3	X
1	6	X
2	15	X
3	24
4	33	X
5	42	X
6	51	X
7	60
8	69	X
9	78	X
10	87	X
11	96