Question

show that exactly one of the number N N + 2 or n + 4 is divisible by 3​

Answer 1

Sol : 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.