Show that exactly one of the number n, n+2 or n+4 is divisible by 3
Answers
Answered by
3
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.
. 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.
Similar questions