+1222 The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
111100111010001ABC01_2.
Compute $A,$ $B,$ and $C$.
+297 Im gonna hard bash it. Its requires extreme patient which I do not have. I shall be using a calculator to shorten the process.
Oh well....
\(N = 2^{20}+2^{19}+2^{18}+2^{17}+2^{14}+2^{13}+2^{12}+2^{10}+2^{6}+A\cdot2^{5}+B\cdot2^{4}+C\cdot2^{3}+2^{1}\)
\(N=1995842+A\cdot2^{5}+B\cdot2^{4}+C\cdot2^{3}\)
\(1995842 \cong 2\mod7\)
\(A\cdot2^{5}+B\cdot2^{4}+C\cdot2^{3}\cong 5\mod7\)
\(32\cong4\mod7,16\cong2\mod7,8\cong1\mod7\)
\(32+8\cong4+1=5\mod7\)
\(A=1,B=0,C=1\)
