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# Question

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I have this question.

I can't figure this out.

Aug 5, 2019

#1
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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 6abc\pmod{13}\\ ab+bc+2ca&\equiv 8abc\pmod {13} \end{align*}

then determine the remainder when $$a+b+c$$ is divided by $$13$$.

Aug 6, 2019