Equation Equivalence

1. Jun 20, 2012

hammonjj

1. The problem statement, all variables and given/known data
Show that:

7x≈3 mod(15)

2. Relevant equations
From the given above I think it should be:

7x-3=15n

3. The attempt at a solution
I tried factoring this in various ways to show that either said was a factor of the other, but I'm struggling here.

But I don't know what to do from here. I actually have several of these problems, but I assume that once I know how to do the first one, they will be easy.

Thoughts? Thanks!
James

2. Jun 20, 2012

Curious3141

Well, for starters, it isn't true in general (for all x).

counterexample: for x = 3, 7*3 = 21 = 6 mod 15

3. Jun 20, 2012

Staff: Mentor

So, since the equation isn't generally true, maybe the aim of the problem was to find the values of x for which it is true.

4. Jun 21, 2012

Curious3141

In which case "Show that:", etc. is a terrible phrasing for it.

5. Jun 21, 2012

HallsofIvy

Yes, it is!

Hammonjj, you want to solve 7x= 3 (mod 15) for x. Of course, that is the same as x= (3/7) (mod 15) so you really just want to know how to write 3/7 in this mod 15 system.

Notice that 7(2)= 14= -1 (mod 15) so that 7(-2)= 1 (mod 15). And, since 15- 2= 13, 1/7= -2= 13 (mod 15). Now, what is 3/7 (mod 15)?

6. Jun 21, 2012

dimension10

Always verify with 0