CBSE Class 10 Answered
prove that one of every three consecutive positive integers is divisible by 3
Asked by rajani.vinod | 26 May, 2019, 11:57: AM
Expert Answer
Let three consecutive positive integers be n, n + 1 and n + 2
when a no. is divided by 3, we can get 0 or 1 or 2 as remainders
so numbers can take the form of 3p, 3p+1 and 3p+2
If n = 3p,
then n is divisible by 3.
If n = 3p + 1,
then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3.
If n = 3p + 2,
then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3
So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3.
Answered by Arun | 26 May, 2019, 05:48: PM
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