Question

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

Answer 1

let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_<r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2



IF n=3qn+4=3q+4n+2=3q+2here n is only divisible by 3
if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3

IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3