# How do you solve for X?

1. Oct 19, 2006

### krispiekr3am

5x = 1 (mod 13)
13x = 2 (mod 23)
37x = 5 (mod 13)

2. Oct 19, 2006

Start off with the definition of 'mod': http://mathworld.wolfram.com/Congruence.html" [Broken].

Last edited by a moderator: May 2, 2017
3. Oct 19, 2006

### 0rthodontist

You could use the chinese remainder theorem if you can put it in the appropriate form. For example if you find some k such that 5k = 1 mod 13 (Euclid's algorithm), then the first equation is x = k (mod 13).

4. Oct 19, 2006

### krispiekr3am

i started with this
5x-1=13y
x=(13y+1)/5
y=1
x then =12/5
is that correct?
-------------------------------
13x-2=23y
x=(23y+2)/13
y=0
x then = 2/13?
-------------------------------

37x-5=13y
x=(13y+5)/37
y=1
x then = 18/37

is that right?

5. Oct 20, 2006

### krispiekr3am

i have created an excel and create a table like this
x 3x module7
1 3 3
2 6 6
3 9 2
4 12 5
5 15 1

What should i do with this graph to do with 13x=2(mod23)

6. Oct 20, 2006

### matt grime

As has been said, use the Chinese remainder theorem (whcih is Euclid's algorithm but dressed up).

Of course if you typed it correctly you're looking for 5x=1 (13) and 37x=5 (13). Are those even compatible? The fact that you've written 37 and not 11 means that either you've mistyped the 13, or you're not happy with modulo arithmetic, and don't see that you can always replace something with something else congruent mod m if it helps.

7. Oct 20, 2006

### CRGreathouse

Nope, $5\not\equiv8\pmod{13}$.

8. Oct 20, 2006

### matt grime

Yes, I know. It was rhetorical/supposed to make the OP think about it, not someone for whom the question is easy.

9. Oct 21, 2006

### krispiekr3am

the answer to 5x = 1 (mod 13) is x = 8 (mod 13)
and the answer to 13x = 2 (mod 23) is x = 9 (mod 23)
and the answer to 37x = 5 (mod 13) is x = 4 (mod 13)

10. Oct 22, 2006

### matt grime

So those aren't sumultaneous equations then? It would greatly benefit you (and would stop you driving your teachers mad) if you wrote things unambiguously, and in full sentences.