Question

state and prove the criterion of divisibility of 11

Answer 1

If that is divisible by 11, so is the original number. So, for instance, 2728 has alternating sum of digits 2-7+2-8 = -11. Since -11 is divisible by 11, so is 2728. Similarly, for 31415, the alternating sum of digits is 3-1+4-1+5 = 10.