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If a,b,c are positive integers less than 13 such that \(\begin{align*} 2ab+bc+ca&\equiv 0\pmod{13}\\ ab+2bc+ca&\equiv 3abc\pmod{13}\\ ab+bc+2ca&\equiv 8abc\pmod {13} \end{align*}\) then determine the remainder when a+b+c is divided by 13.

 Jul 27, 2022
 #1
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Question answered by heureka and Alan here : https://web2.0calc.com/questions/help-me_17340

cool

 Jul 27, 2022
 #3
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apparently it was 0

brainiac  Jul 27, 2022
 #2
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For this problem, you can just find specific values that work.  Here, you can check that a = 2, b = 6, and c = 10 work.  Since 2 + 6 + 10 = 18 = 5 (mod 13), the answer is 5.

 Jul 27, 2022

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