Math, asked by akhila123487, 9 months ago

7. show that one and only one out of
n, (n+1),(n+2) is divisible by 3.
where 'n' is any positive insteger.​

Answers

Answered by bhartipuran24
0

Answer:

according to Euclid division algorithm

if x = 3 is any positive integer then we can wright it

x= n

x= n+ 1

x = n + 2

then we can say that only one of them is divisible by 3

Answered by anandsinghreso
1

Step-by-step explanation:

let n be any integer

If n=3k,then

n+1=3k+1,not divisible by 3

n+2=3k+2,not divisible by 3

If n=3k+1(not divisible by 3),then

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

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

If n=3k+2(not divisible by 3),then

n+1=3k+3=3(k+1),divisible by 3

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

Hence by seeing all the above cases,we can safely say that:out of n,n+1 and n+2,only one is divisible by 3.

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