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If a, b, and c are positive integers less than 13 such that: 

2ab + bc + ca ≡ 0 (mod 13)

ab + 2bc + ca ≡ 3abc (mod 13)

ab + bc + 2ca ≡ 8abc (mod 13)

What is the remainder when a + b + c is divided by 13?

 

Thanks in advance!

 Jun 23, 2024
 #1
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Hopefully this is helpful, https://web2.0calc.com/questions/hard-hard-hard. It might be wrong, and it might not answer them all, but i hope this helps

 Jun 23, 2024
 #2
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I want a helpful solution, I'm not trying to brute force it with Wolfram Alpha. Thanks though!

 Jun 24, 2024

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