Question: Show that IOn = 4 mod 6 for all n ~ 1, and hence that if m = n mod 6 then 10m = IOn

Show that IOn = 4 mod 6 for all n ~ 1, and hence that if m = n mod 6 then 10m = IOn mod 7.

From this determine the remainder when 1010 + 10(102

) + 10(103

) + ... + 10(1010

) is divided by 7.

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