Lizzie came up with a divisibility test for a certain number $m$ which is not equal to $1$ :
- Break a positive integer 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 $64 - 47 + 35 = 52.$)
Finally, 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 $m$).
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.
