Problem 5: Prove cach of the following statements. 1. 2 divides n +n whenever n is a positive integer. 2. 3 divides n'+ 2n whenever n is a positive integer 3. 5 divides n'-n whenever n is a nonnegative integer 4. 6 divides n'-n whenever n is a nonnegative integer

Problem 5: Prove cach of the following statements. 1. 2 divides n +n whenever n is a positive integer. 2. 3 divides n'+ 2n whenever n is a positive integer 3. 5 divides n'-n whenever n is a nonnegative integer 4. 6 divides n'-n whenever n is a nonnegative integer

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 21PE

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Concept explainers

Operations

In mathematics and computer science, an operation is an event that is carried out to satisfy a given task. Basic operations of a computer system are input, processing, output, storage, and control.

Basic Operators

An operator is a symbol that indicates an operation to be performed. We are familiar with operators in mathematics; operators used in computer programming are—in many ways—similar to mathematical operators.

Division Operator

We all learnt about division—and the division operator—in school. You probably know of both these symbols as representing division:

Modulus Operator

Modulus can be represented either as (mod or modulo) in computing operation. Modulus comes under arithmetic operations. Any number or variable which produces absolute value is modulus functionality. Magnitude of any function is totally changed by modulo operator as it changes even negative value to positive.

Operators

In the realm of programming, operators refer to the symbols that perform some function. They are tasked with instructing the compiler on the type of action that needs to be performed on the values passed as operands. Operators can be used in mathematical formulas and equations. In programming languages like Python, C, and Java, a variety of operators are defined.

Question

Problem 5: Prove each of the following statements.
1. 2 divides n2 + n whenever n is a positive integer.
2. 3 divides n + 2n whenever n is a positive integer
3. 5 divides n° – n whenever n is a nonnegative integer
4. 6 divides n³ – n whenever n is a nonnegative integer

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