Prove that every 6-digit integer of the form abcabc (ex. 241241, 638638) is divisible by 13.
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The decimal expansion of $\displaystyle abcabc$, is $\displaystyle a\cdot10^5+b\cdot10^4+c\cdot10^3+a\cdot10^2+b\cdot 10+c=10^3(a\cdot10^2+b\cdot10+c)+a\cdot10^2+b\cdot 10+c$.
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