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Lizzie came up with a divisibility test for a certain number : m not equal to 1

 

Break a positive integer n into two-digit chunks, starting from the ones place. (For example, the number 354764 would break into the two-digit chunks 64,47,35)

 

Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be 64-47+35=52)

 

Find m and show that this is indeed a divisibility test for m (by showing that n is divisible by m if and only if the result of this process is divisible by m).

 Jul 13, 2022
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This is a divisibility rule for 11. Here's more information about divisibility rules:

 

https://en.wikipedia.org/wiki/Divisibility_rule#:~:text=If%20the%20number%20of%20digits,must%20be%20divisible%20by%2011.&text=If%20the%20number%20of%20digits%20is%20odd%2C%20subtract%20the%20first,must%20be%20divisible%20by%2011.

 Jul 13, 2022

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