Prove that one of three consecutive integers divisible by 3, Mathematics

Prove that one of every three consecutive integers is divisible by 3.

Ans:

n,n+1,n+2 be three consecutive positive integers

We know that n is of the form 3q, 3q +1, 3q + 2

So we have the following cases

Case - I     when n = 3q

In the this case, n is divisible by 3 but n + 1 and n + 2 are not divisible by 3

Case -  II   When n = 3q + 1

Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not divisible by 3

Case - III When n = 3q +2

Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not divisible by 3

Hence one of n, n + 1 and n + 2 is divisible by 3

Posted Date: 4/8/2013 1:02:56 AM | Location : United States







Related Discussions:- Prove that one of three consecutive integers divisible by 3, Assignment Help, Ask Question on Prove that one of three consecutive integers divisible by 3, Get Answer, Expert's Help, Prove that one of three consecutive integers divisible by 3 Discussions

Write discussion on Prove that one of three consecutive integers divisible by 3
Your posts are moderated
Related Questions
What is Matrices?


Application of Probability in Business 1. Business games of chance for illustration, Raffles Lotteries. 2. Insurance firms: this is generally done when a new client or prop

there is 22 owls . my mom gave me 6 more . how many owls do they have

Objectives :  After studying this unit, you should be able to : 1.   explain the processes involved in counting; 2.   explain why the ability to recite number names is no in

HOW MANY ZERO ARE THERE AT THE END OF 200


Solve the subsequent LP problem graphically through enumerating the corner points. MAX:              3X1 + 4X2 Subject to:    X1   12                     X2    10

what is greater than three forths

When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years.  Find their present