Something i have been thinking about..

So take the multiple of 9 : 9,18,27,36 etc.. and one thing we notice is that if we keep adding digits up repeatedly they come to 9, so you have a simple divisibility test. Presumably, this works because 9 is one less than the base we are working in which is 10.

Does it follow if we work in other bases, e.g. base 5 and look at multiples of 4 that the digits add up to 4?

It appears so, upon a few test cases? Is this generally going to be true for other bases? Is this a theorem?

So take the multiple of 9 : 9,18,27,36 etc.. and one thing we notice is that if we keep adding digits up repeatedly they come to 9, so you have a simple divisibility test. Presumably, this works because 9 is one less than the base we are working in which is 10.

Does it follow if we work in other bases, e.g. base 5 and look at multiples of 4 that the digits add up to 4?

It appears so, upon a few test cases? Is this generally going to be true for other bases? Is this a theorem?

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