Question

if n is a natural number, then exactly one of numbers n, n+2 and n+1 must be a multiple of
​

Answer 1

Answer:

3

Step-by-step explanation:

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Answer 2

Given :  n is a natural number,

To Find : exactly one of numbers n, n + 2 and n + 1 must be a multiple of​ what

Solution:

exactly one of numbers n, n + 2 and n + 1 must be a multiple of​  3

Here is the proof

Without losing generality any natural number can be represent in the form

3k , 3k -1 , 3k - 2   where  k is natural number

Using 3k

n = 3k   is divisible by 3

n + 1 = 3k + 1  is not divisible by 3

n + 2 = 3k + 2  is not divisible by 3

Exactly one is divisible by 3

Using 3k+1

n = 3k+1   is  not divisible by 3

n + 1 = 3k + 1  + 1 = 3k + 2 is not divisible by 3

n + 2 = 3k + 1+ 2 = 3k + 3 = 3(k + 1)   is  divisible by 3

Exactly one is divisible by 3

Using 3k+2

n = 3k+2  is  not divisible by 3

n + 1 = 3k + 2  + 1 =  3k + 3 = 3(k + 1)   is  divisible by 3

n + 2 = 3k +2+ 2 = 3k + 4 = 3(k + 1) + 1  is  not divisible by 3

Exactly one is divisible by 3

Hence If n is a natural number, then exactly one of numbers n, n + 2 and n + 1 must be a multiple of​ 3

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