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CBSE Class 10 Answered

Show that one and only one out of n,n+2 or n+4 is divisible by 3 where n is any positive integer.
Asked by mehaksaini | 04 Feb, 2010, 11:16: AM
answered-by-expert Expert Answer

To prove n , n+2 or n+4 is divisible by 3,

Case 1 Let n is divisible by 3

So n = 3k for some positive integer k

Now n+2 = 3k+2 which is not divisible by 3

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

Case 2 n+2 is divisible by 3  so

n+2 =3k

so n =3k-2  not divisible by  3

n+4 = 3k+2 = not divisible by  3

Case 3: Let n+4 is divisible by 3 so n+4 = 3k

n =3k-4=3(k-1)-1=3m-1 not divisible by 3

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

Answered by | 30 Nov, 2017, 12:12: PM
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