Prove that an integer is divisible by 11 if and only if the difference between the sum of the digits in the units place, the hundreds place, the ten thousands place, (the places corresponding to the even powers of 10) and the sum of the digits in the tens place, the thousands place, the hundred thousands place, (the places corresponding to the odd powers of 10) is divisible by 11. (Hint: 10 = 11 – 1, 100 99 + 1, 1000 = 1001 – 1, 10000 = 9999 + 1, etc. What can you say about the integers 11, 99, 1001, 9999, etc. as far as divisibility by 11 is concerned?)
