this post was submitted on 04 Nov 2024
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Never realized there are so many rules for divisibility. This post fits in this category:
299,999 would be 999 - 299 = 700 which is divisible by 7. And if we simply swap grouped digits to 999,299, it is also divisible by 7 since 299 - 999 = -700.
And as for 13:
So we have 999 - 999 + 299 = 299.
You can continue with other rules so we can then take this
So for 299 it's 29 + 9 * 4 = 65 which divides by 13. Pretty cool.
That is indeed an absurd amount of rules (specially for 7) !
It should be fun to develop each proof. Particularly the 1,3,2,-1,-3,-2 rule, which at first sight seems could be easily expanded to any other number.