KöMaL 2005 B3863

Show that the number $1^{2006}-2^{2006}+3^{2006}-4^{2006}+\ldots-2004^{2006}+2005^{2006}$ is divisible by 1003. Is it also divisible by 2006?

Official text KöMaL. Quoted with source.

Solutions

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