Number Theory

I didn't follow an algorithm. I legit tried every single possibilitility until I found 1. 

When wee have A, B, C = 1, 0, 1, we get the number $10011010011101110$

Converting this into base 10, we have

$(10011010011101110)_2 = (1 × 2^{16}) + (0 × 2^{15}) + (0 × 2^{14}) + (1 × 2^{13}) + \\(1 × 2^{12}) + (0 × 2^{11}) + (1 × 2^{10}) + (0 × 2^9) + (0 × 2^8) + \\(1 × 2^7) + (1 × 2^6) + (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + \\(1 × 2^2) + (1 × 2^1) + (0 × 2^0) = (79086)_{10}$

Dividing by 7, we get $79086/7=11298$

THUS, 

The answer is $(A, B, C) = (1, 0, 1)$

Thanks! :)

*I'm so tired