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14-03-2019
Mathematics

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Show that any number of the form ABCABC (e.g. 356356) is divisible by 13.

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LammettHash LammettHash

14-03-2019

We could write such a number as

[tex]10^5a+10^4b+10^3c+10^2a+10b+c[/tex]

[tex]=10^2(10^3+1)a+10(10^3+1)b+(10^3+1)c[/tex]

[tex]=(10^3+1)(100a+10b+c)[/tex]

[tex]10^3+1=1001=13\cdot77[/tex] so we're done.

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