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> Consider the $10$ million $7$-digit numbers, where numbers smaller than one million have been padded with zeros on the left to make them $7$ digits long as well: $$\{0000000, 0000001,\ldots, 0000099, 0000100,\ldots,0999999,1000000,\ldots,9999998,9999999\}.$$ Let $N$ be a $70$ million digit number formed by concatenating these $10$ million $7$-digit numbers together in any order. Prove that $N$ is a multiple of $239$.
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I didn't see how to use the fact that $N$ is a concatenation of these strings to prove divisibility by the prime $239$. How can we do that?