MATHEMATICS

Sabtu, 12 November 2011

Numbers divisible by seven

Sometimes, doing an exercise runs out of control, slurps time and leads to posts like this:

\begin{array}{l}
111111101101010101001001 \\
111111101101001001010101 \\
111111010101101101001001 \\
111111010101001001101101 \\
111111001001101101010101 \\
111111001001010101101101 \\
101101111111010101001001 \\
101101111111001001010101 \\
101101010101111111001001 \\
101101010101001001111111 \\
101101001001111111010101 \\
101101001001010101111111 \\
10101111111101101001001 \\
10101111111001001101101 \\
10101101101111111001001 \\
10101101101001001111111 \\
10101001001111111101101 \\
10101001001101101111111 \\
1001111111101101010101 \\
1001111111010101101101 \\
1001101101111111010101 \\
1001101101010101111111 \\
1001010101111111101101 \\
1001010101101101111111
\end{array}

you might assume they are binary numbers. They might be, but they are just ordinary decimal numbers consisting of only ones and zeros. They are all divisible by seven. For your convenience I'll show them again, divided by seven this time.

\begin{array}{l}
15873014443001443000143 \\
15873014443000143001443 \\
15873001443014443000143 \\
15873001443000143014443 \\
15873000143014443001443 \\
15873000143001443014443 \\
14443015873001443000143 \\
14443015873000143001443 \\
14443001443015873000143 \\
14443001443000143015873 \\
14443000143015873001443 \\
14443000143001443015873 \\
1443015873014443000143 \\
1443015873000143014443 \\
1443014443015873000143 \\
1443014443000143015873 \\
1443000143015873014443 \\
1443000143014443015873 \\
143015873014443001443 \\
143015873001443014443 \\
143014443015873001443 \\
143014443001443015873 \\
143001443015873014443 \\
143001443014443015873
\end{array}

Even mathematics tries to steal your time, sometimes.

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