How Do You Solve 7x ≡ 3 (mod 15)?

[hammonjj]

Homework Statement

Show that:

7x≈3 mod(15)

Homework Equations

From the given above I think it should be:

7x-3=15n

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

 

[Curious3141]

Homework Statement

Show that:

7x≈3 mod(15)

Homework Equations

From the given above I think it should be:

7x-3=15n

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

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

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

 

[Mark44]

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.

 

[Curious3141]

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.

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

 

[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)?

 

[dimension10]

Homework Statement

Show that:

7x≈3 mod(15)

Homework Equations

From the given above I think it should be:

7x-3=15n

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

Always verify with 0