(b) Let n be an integer. Show that n if the sum of the digits of n is a multiple of 3, then n is a multiple of 3. You must do so by a direct proof. For this problem you may assume that ∀a, b ∈ Z, ∀m ∈ Z+, (a ≡ x (mod m) ∧ b ≡ y (mod m)) ⇒ ab ≡ xy mod m. *Solve by direct proof*

(b) Let n be an integer. Show that n if the sum of the digits of n is a multiple of 3, then n is a multiple of 3. You must do so by a direct proof. For this problem you may assume that ∀a, b ∈ Z, ∀m ∈ Z+, (a ≡ x (mod m) ∧ b ≡ y (mod m)) ⇒ ab ≡ xy mod m. Solve by direct proof

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section: Chapter Questions

Problem 15RP

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Concept explainers

Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

Question

(b) Let n be an integer. Show that n if the sum of the digits of n is a multiple of 3,
then n is a multiple of 3. You must do so by a direct proof. For this problem you
may assume that ∀a, b ∈ Z, ∀m ∈ Z+, (a ≡ x (mod m) ∧ b ≡ y (mod m)) ⇒ ab ≡ xy
mod m. *Solve by direct proof*

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