Observe that 7524 = 71000 + 5100 + 210 + 4 = 7(999 + 1) + 5(99 + 1) + 2(9 + 1) + 4 =
Chapter 4, Problem 47(choose chapter or problem)
Observe that 7524 = 71000 + 5100 + 210 + 4 = 7(999 + 1) + 5(99 + 1) + 2(9 + 1) + 4 = (7999 + 7) + (599 + 5) + (29 + 2) + 4 = (7999 + 599 + 29) + (7 + 5 + 2 + 4) = (71119 + 5119 + 29) + (7 + 5 + 2 + 4) = (7111 + 511 + 2)9 + (7 + 5 + 2 + 4) = (an integer divisible by 9) + (the sum of the digits of 7524). Since the sum of the digits of 7524 is divisible by 9, 7524 can be written as a sum of two integers each of which is divisible by 9. It follows from exercise 15 that 7524 is divisible by 9. Generalize the argument given in this example to any nonnegative integer n. In other words, prove that for any nonnegative integer n, if the sum of the digits of n is divisible by 9, then n is divisible by 9.
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