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Let n be a positive integer. We write x; for the ith digit of n. (I.e., if n = 217, then x1 = 7, x2 = 1 and x3 = 2.) In particular, n = x1 + x210+ + xk10k-1. Prove the following: (a) n = x1 + x2+ ...+ xk( mod 9). (b) n = x1 – x2 +...+ (-1)k-lxk( mod 11).

Let n be a positive integer. We write x; for the ith digit of n. (I.e., if n = 217, then x1 = 7, x2 = 1 and x3 = 2.) In particular, n = x1 + x210+ + xk10k-1. Prove the following: (a) n = x1 + x2+ ...+ xk( mod 9). (b) n = x1 – x2 +...+ (-1)k-lxk( mod 11).

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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Let n be a positive integer. We write x; for the ith digit of n. (I.e., if n = 217, then x1 = 7, x2 = 1 and x3 = 2.) In particular, n = x1 + x210+ + xk10k-1. Prove the following: (a) n = x1 + x2+ ...+ xk( mod 9). (b) n = x1 – x2 +...+ (-1)k-lxk( mod 11).
Transcribed Image Text:Let n be a positive integer. We write x; for the ith digit of n. (I.e., if n = 217, then x1 = 7, x2 = 1 and x3 = 2.) In particular, n = x1 + x210+ + xk10k-1. Prove the following: (a) n = x1 + x2+ ...+ xk( mod 9). (b) n = x1 – x2 +...+ (-1)k-lxk( mod 11).
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