Please do part c and please include a general proof with a general solution. Please show step by step and explain

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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Please do part c and please include a general proof with a general solution. Please show step by step and explain

(a) Take any decimal integer, write the digits in reverse order, and subtract
the reversed number from the original number. Show that the result is
always divisible by 9.
(b) If the decimal integer has an odd number of digits, show that the result
obtained in (a) will always be divisible by 99.
(c) Show that if you take any decimal integer n, rearrange the digits, multi-
ply by any power of 10, and subtract n from the resulting number, then
your final result will always be divisible by 9.
Transcribed Image Text:(a) Take any decimal integer, write the digits in reverse order, and subtract the reversed number from the original number. Show that the result is always divisible by 9. (b) If the decimal integer has an odd number of digits, show that the result obtained in (a) will always be divisible by 99. (c) Show that if you take any decimal integer n, rearrange the digits, multi- ply by any power of 10, and subtract n from the resulting number, then your final result will always be divisible by 9.
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