Lizzie came up with a divisibility test for a certain number m: Break a positive integer n into two-digit chunks, starting from the one's 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).