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
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. H v (~T > R) 2. Hv (E > F) 3. ~T v E 4. ~H & D / R v F INSTRUCTIONS: Con

Write following in terms of simpler logarithms.  (a) log 3 (9 x 4    / √y) Solution log 3 (9 x 4 / √y) =log ­ 3 9x 4 -  log  y (1/2) =log ­ 3 9 + log ­ 3 x 4

How do I increase and decrease tax and sales

What is Converse, Inverse, and Contrapositive In geometry, many declarations are written in conditional form "If ...., then....." For Example: "If two angles are right angles,

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

if Mr.Ibias oredered a rectangular pizza and he wants 2/3 of the pizza to be pepperoni and 1/2 of the pizza with pineapple draw and label the pizza with toppings explain your think

Advantages and disadvantages of operation researchs

Domain of a Vector Function There is a Vector function of a single variable in R 2 and R 3 have the form, r → (t) = {f (t), g(t)} r → (t) = {f (t) , g(t), h(t)} co

If X = {a, e, i, o, u} and Y = {a, b, c, d, e}, then what is Y - X ?

A Pythagorean triple is a set of positive integers (a,b,c) like  a2 + b2 = c2.  Write a function "ispythag" that will receive 3 positive integers (a, b, c in that order) and will r