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$$ x \equiv -74 \ mod \ 31 $$

According to Google & Wolframalpha the answer is 19

Following the method in this answer and using this answer I get 12. Using my calculator with this answer yeilds 12 also.

What answer is right? If the web is correct, how do they come about that answer?

Community
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Ewan
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  • Note that $-74 = -3(31) + 19$. So, $19$ looks like the correct answer here. Could you show your work for "following the method" in those answers? – Ben Grossmann Dec 12 '14 at 21:26
  • 19 is certainly not "the (correct) answer". At best it is a correct answer, and at worst not correct. But that depends on what the question is, which you have not stated. – fkraiem Dec 12 '14 at 21:58
  • @fkraiem of the answers provided, $19$ is the correct one – Ben Grossmann Dec 12 '14 at 22:03

1 Answers1

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$x\equiv -74 \equiv -74+31 \equiv -43\equiv -43+31 \equiv -12 \equiv -12+31 \equiv 19 $

CryoDrakon
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  • Am getting confused between the 12 and the 19 aren't I? ... – Ewan Dec 12 '14 at 21:30
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    When I started to learn modulo and I get a negative value I just kept adding the modulo until I get a positive number. So you get -12 not 12. I dont know how you got 12 with your calculator... – CryoDrakon Dec 12 '14 at 21:34