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
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
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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