Question

show that one and only one of n,+ n+2 ,n+4 is divisible by 3 , where n is any positive integer.​

Answer 1

Answer:

We applied Euclid Division algorithm on n and 3. a = bq +r on putting a = n and b = 3 n = 3q +r , 0<r<3 i.e n = 3q -------- (1),n = 3q +1 --------- (2), n = 3q +2 -----------(3) n = 3q is divisible by 3 or n +2 = 3q +1+2 = 3q +3 also divisible by 3 or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3 Hence n, n+2 , n+4 are divisible by 3.

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