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  3. a3 the number did2do has nine not necessarily dis tinct...

Question: a3 the number did2do has nine not necessarily dis tinct...

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A-3 The number did2...do has nine (not necessarily dis- tinct) decimal digits. The number eje2...e is such that each of the nine 9-digit numbers formed by replacing just one of the digits di is did2...dy by the correspond ing digit e (1<i<9) is divisible by 7. The number fif2...fo is related to eje2...es is the same way: that is, each of the nine numbers formed by replacing one of the e; by the corresponding fi is divisible by 7. Show that, for each i, di- fi is divisible by 7. [For example, if did2...do 199501996, then e6 may be 2 or 9, since 199502996 and 199509996 are multiples of 7.]
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