modular arithmetic question

Coefficient

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Jan 30, 2020
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Hi,
I'm stuck on this question: solve for x (x is an integer) 7x = -19 mod(9) .

Thank you for your help.
 

Dr.Peterson

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I would start by rewriting -19 as a smaller number (mod 9). What is -19 congruent to? That is not necessary, but will make things easier.

Then you can just try numbers 1 through 8 to see if any yield a product congruent to the number you found.
 

Coefficient

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i tried this :

7x ≡ -19[9]
7x ≡ -10[9]
7x ≡ -1[9]
7x ≡ 8[9]

But i couldn't understand how this would help me because the next question is to deduce the solutions of the equation : 7x-9y= -19

Thanks.
 

topsquark

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Aug 27, 2012
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i tried this :

7x ≡ -19[9]
7x ≡ -10[9]
7x ≡ -1[9]
7x ≡ 8[9]

But i couldn't understand how this would help me because the next question is to deduce the solutions of the equation : 7x-9y= -19

Thanks.
Note that 9y = 0 (mod 9). So the solutions for 7x - 9y = -19 (mod 9) will be the solutions for 7x = -19 (mod 9) and y = anything.

-Dan
 

Coefficient

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Note that 9y = 0 (mod 9). So the solutions for 7x - 9y = -19 (mod 9) will be the solutions for 7x = -19 (mod 9) and y = anything.

-Dan
Thank you
 

Jomo

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What does 7x ≡ 8[9] mean? If I remember correctly it means that 7x-8 = 9k, where k is an integer. So solve for x.

7x = 9k+8, then x= (9k+8)/7. Now find k so that (9k+8)/7 is an integer.
 

Jomo

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So what answer did you get??
 
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