# Stumped on a Proof

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• September 3rd 2010, 07:08 PM
MATNTRNG
Stumped on a Proof
Prove that every 6-digit integer of the form abcabc (ex. 241241, 638638) is divisible by 13.
• September 3rd 2010, 07:46 PM
melese
The decimal expansion of $abcabc$, is $a\cdot10^5+b\cdot10^4+c\cdot10^3+a\cdot10^2+b\cdot 10+c=10^3(a\cdot10^2+b\cdot10+c)+a\cdot10^2+b\cdot 10+c$.