Since we are to use the condition that 3 does not divide n, we have: n/3 = q +r/3 n = 3q + r where q is the quotient and r is the remainder and not divisible by 3 or equal to 0 both q and r are whole numbers
Substituting, 2(3q + r) (q + r/3) + 1/3 6q² + 4qr + 2r²/3 + 1/3 6q² + 4qr + (2r² + 1)/3 The term: (2r² + 1)/3 will only be a whole number if r is not divisible by 3 or equal to 0, which means that (2n² + 1)/3 is a whole number if and only if n/3 is not a whole number
