I am really stuck on this question, can someone help?

Lizzie came up with a divisibility test for a certain numberm=1:

• Break a positive integern into two-digit chunks, starting from the ones place. (For example, the number354764would break into the two-digit chunks64, 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)

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