Difference between revisions of "Divisibility rules/Rule 1 for 7 proof"
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Revision as of 11:30, 25 November 2023
Proof
This is based on divisibility by 11 rule
Assume N has 3k digits, otherwise add zeros to the left. WLOG let where the are base-ten numbers. Then Rewriting as 3 digit numbers, that is, partitioning into 3 digit numbers ().
Since ,
This is the alternating sum of groups of 3 digit numbers of , which is what we wanted.