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Popular >

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

Solution

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

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