# Octal divisibility

In base $$10$$, there are simple divisibility rules formulated for division by $$2,3,4,5,6,8,9$$ and $$11$$ based on last digit, sum of digits or difference of alternate digits,(i.e., all numbers less than or equal to $$(10+1)$$. The number $$1$$ is of course ignored in this context.

Which is the only number less than or equal to $$9_{10}=11_{8}$$, for which a divisibility rule cannot be formulated in base $$8$$, based on the either last digit(s), sum of digits or difference of alternate digit sums. The answer is to be given in base $$10$$?.

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