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denote n=akak-1...a0 in terms of its digits (not a product) where a0 is its last

ID: 2987526 • Letter: D

Question

denote n=akak-1...a0 in terms of its digits (not a product) where a0 is its last digit, a1 is the second last didgit, and so on. let n1= (akak-1...a1)-2a0. prove that n is divisible by 7 if and only if n1 is. Please note that if and only iff means you have to prove in BOTH directions.

(Divisibility rule for 7) We know easily when an integer is divisible by 2,3 or 5 without (directly) applying division. For example, an integer is divisible by 3 if and only if the sum of its digits is. This exercise concerns the rule for 7.

Explanation / Answer

Form the alternating sum of blocks of three from right to left. 1,369,851: 851 ? 369 + 1 = 483 = 7

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