Solve 6x ≡ 9 (mod 21).

Question

Solve 6x  ≡ 9 (mod 21).

amistre64 · Answer

6x/21 = nR9

right?

anonymous · Answer

ok

amistre64 · Answer

reduce it all by a factor of 3 maybe ... 

2x/7 = n R3 ??  i dont do mods enough to be confident in them

amistre64 · Answer

9
9 +21 =  30 <-  heres one
30+21 = 51
51+21 = 72 <- heres one
72+21 = 93
93+21 = 114 <- heres one

seems to be a pattern

amistre64 · Answer

6(5,12,19,...)

anonymous · Answer

right what amistre said. you can write 
$$6x\equiv 9(21)$$
$$6x\equiv 30(21)$$
$$x\equiv 5(21)$$

amistre64 · Answer

6(5+7n) ; n>=0 maybe

myininaya · Answer

$$6x=9+21k$$
I like to enter in values of k to see what makes x an integer
k=0 => x not integer
k=1 => x=5
k=2 => x not integer
k=3 => x=12
k=4 => x not integer
k=5 => x=19
k=6 => x not intger
k=7 => x=26
so there is a pattern
x=5+7i for any integer i

anonymous · Answer

oh did i screw up?  maybe 
$$6x\equiv 9(21)$$
$$2x\equiv 3(7)$$
$$2x\equiv 10(7)$$
$$x\equiv 5(7)$$ is a better answer

amistre64 · Answer

i saw that but wasnt gonna say nuthin ;)

anonymous · Answer

lol 
back to the dungeon for me