# What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

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## 7 Replies - 1190 Views - Last Post: 11 October 2012 - 07:59 AM

### #1 deprosun

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# What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 01:45 PM

I know how to get the inverse of 3(mod 7), and thats about it.
What is the procedure to solve this?
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## Replies To: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

### #2 macosxnerd101

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 01:46 PM

What is the remainder of 3 when you divide it by 7?

### #3 deprosun

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 01:53 PM

macosxnerd101, on 28 September 2012 - 03:46 PM, said:

What is the remainder of 3 when you divide it by 7?

3

This post has been edited by deprosun: 28 September 2012 - 01:54 PM

### #4 blackcompe

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 02:06 PM

Ask yourself what number, x, times 3 mod 7 will give you 4?

3x ≡ 4 mod 7 # 4 mod 7 equals 4
3x mod 7 = 4 # what x makes this true
x = 6

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### #5 macosxnerd101

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 03:48 PM

Sorry, I didn't see the congruence in the title! Make sure to include these things in your post as well.

### #6 deprosun

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 03:53 PM

macosxnerd101, on 28 September 2012 - 05:48 PM, said:

Sorry, I didn't see the congruence in the title! Make sure to include these things in your post as well.

I think I did . Sorry if I wasnt clear enough.
Oh! BTW, how do you set this mathematical form. My brain in freezing; logarithm of 7 to the base 2 modulo 19

### #7 macosxnerd101

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 28 September 2012 - 07:21 PM

Modular arithmetic is limited to the integers. Remember that log2(7) returns a real number.

### #8 deprosun

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## Re: What are the solutions of the linear congruence 3x ≡ 4 (mod 7)?

Posted 11 October 2012 - 07:59 AM

Thank you all