Thread: Modular Arithmetic- Quick question

Hello

I've been having difficulty with understanding a concept within modular arithmetic

The question I have been stuck on for a while now is:

Given 5x = -2(mod 8)

find x^2(mod 8)

My attempt at a solution:

5x = -2(mod 8)'
25x^2 = 4 (mod 8)
x^2 = 4 (mod 8), as 25 = 4 (mod 8)

The answer at the back says 1, and I'm not sure where I went wrong

Thanks in advance

Originally Posted by Wandering

Hello

I've been having difficulty with understanding a concept within modular arithmetic

The question I have been stuck on for a while now is:
i can't find a mistake. for example x=6 satisfies 5x=-2(mod 8) and 6^2=4(mod 8)
Given 5x = -2(mod 8)

find x^2(mod 8)

My attempt at a solution:

5x = -2(mod 8)'
25x^2 = 4 (mod 8)
x^2 = 4 (mod 8), as 25 = 4 (mod 8)

The answer at the back says 1, and I'm not sure where I went wrong

Thanks in advance

i can't find a mistake. for example x=6 satisfies 5x=-2(mod 8) and 6^2=4(mod 8)

So the answer at the back must be wrong?

Thanks a lot

Originally Posted by Wandering

Hello

I've been having difficulty with understanding a concept within modular arithmetic

The question I have been stuck on for a while now is:

Given 5x = -2(mod 8)

find x^2(mod 8)

My attempt at a solution:

5x = -2(mod 8)'
25x^2 = 4 (mod 8)
x^2 = 4 (mod 8), as 25 = 4 (mod 8)

The answer at the back says 1, and I'm not sure where I went wrong

Thanks in advance

I too agree with your answer, nice going!

One little thing which I'm presuming is a typo since you got the correct answer. You wrote 25 = 4 (mod 8). In actuality 25 = 1 (mod 8).

-Dan

Hello, Wandering!

Sometimes early squaring can introduce extraneous roots.
So I solved it head-on.

. .

. .





You are correct . . . Good work!