POW #7: Divisible by 7

Consider the following:

91 and 9 - (2)(1) = 7 are each divisible by 7.

385 and 38 - (2)(5) = 28 are each divisible by 7.

4816 and 481 - (2)(6) = 469 are each divisible by 7.

What generalization do these facts suggest? Write out this generalization in careful notation, and then prove it.

Return solutions ON PAPER to Laura Taalman, Burruss 127, by 4/21/05.
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