en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Word Problems >

Show that 1 greater than the sum of the squares of any three consecutive integers is always divisible by 3.

Solution

prove

t ha t 1 g re a t er t han t h e s u m o f t h e s q u a res o f an y t h ree co n sec u t i v e in t e g ers i s a lw a ys d i v i s ib l e b y 3.

Solution

The numbers : - 1, 0, 1

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number 1 : x + 1

Consecutive number 2 : x + 2

A.T.Q.:

1 + x^{2} + (x + 1)^{2} + (x + 2)^{2} = 3

Solve

1 + x^{2} + (x + 1)^{2} + (x + 2)^{2} = 3 : x = - 1

x + 1 = - 1 + 1 = 0

x + 2 = - 1 + 2 = 1

The numbers : - 1, 0, 1

Popular Examples

Three increased by the product of a number and 6 is greater than-21 In 2 years, Martin wants to buy a bicycle that costs 700.00. If he opens a savings account that earns 13% interest compounded monthly, how much will he have to deposit as principal to have enough money in 2 years to buy the bike?5 more than 2 times a number The circumference of a circle is 24pi m. What is the area, in square meters? Express your answer in terms of pipi.The circumference of a circle is 20pipi cm. Find its diameter, in centimeters.