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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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