How Do You Solve 7x ≡ 3 (mod 15)?

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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
 
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hammonjj said:

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
 
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.
 
Mark44 said:
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.
 
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)?
 
hammonjj said:

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
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

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