Lizzie came up with a divisibility test for a certain number \(m \neq 1\): 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).
I need help can anyone show me the steps to solve this
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.
