Question

Prove thta only one of the numbers n-1 ,n+1 or n+3 is divisible by 3, where , n is any positive integer.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Okay so any no. Will be divisible by 3 if its of the form 3m where m is any positive integer. Now if n-1 is divisble by 3 it will be of the 3m therefore n-1=3m

n=3m+1

Now n+1 will be 3m+2 which is not divisible by 3

And n+3 will be 3m+4 again not divisble by 3

Now lets assume n+1 is divisble by 3; it will be of the form 3m.therefore n+1=3m; n=3m-1;

Now n-1 will be 3m-2 and n+3 will be n=3m-4 again not divisible by 3. Hence in the same way if n+3 is divisible by 3 then n+3=3m; n=3m-3; now n+1=3m-2 and n-1=3m-4 so hence it can be shown that only one of the following can be divisible by 3.