What is a quick way to prove using induction the following fact: "A number is a multiple of 11 if and only if the sum of its even-placed digits minus the sum of its odd-placed digits is also a multiple of 11"?
Thanks in advance.
2026-04-13 19:44:46.1776109486
Divisibility criterion for 11
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Hint:
Use congruences. $10\equiv -1\mod11$.