Question

show that only one of one and one out of p,p+2,p+4 is divisible by 3

Answer 1

Member since Apr 11 2014

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