# Modular Arithmetic- Quick question

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• Apr 30th 2011, 02:55 PM
Wandering
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
• Apr 30th 2011, 03:03 PM
abhishekkgp
Quote:

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)
• Apr 30th 2011, 03:29 PM
Wandering
So the answer at the back must be wrong?

Thanks a lot
• Apr 30th 2011, 03:45 PM
topsquark
Quote:

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
• Apr 30th 2011, 05:12 PM
Soroban