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Integer divisible by numbers obtained by deleting its digits

Source: XIV Rioplatense Mathematical Olympiad (2005), Level 3

July 26, 2011
number theory unsolvednumber theory

Problem Statement

Find the largest positive integer nn not divisible by 1010 which is a multiple of each of the numbers obtained by deleting two consecutive digits (neither of them in the first or last position) of nn. (Note: nn is written in the usual base ten notation.)
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