If n is a natural number then n2+n+3 is odd. This is what I have and wanted to know if I was doing it right or not: Let n be a member of the natural numbers. If n is even, then n=2k, k member of natural numbers, and n2+n+3 =(2k)2+2k+3 =4k2+2k+3 = 2(2k2+k+1)+1, where (2k2+k+1) is a member of the natural numers. This means that when n is even, n2+n+3 is odd. If n is odd, then n=2j+1 where j is a member of the natural numbers and n2+n+3 =(2j+1)2+(2j+1)+3 =4j2+4j+1+2j+4 =4j2+6j+5 =2(2j2+3j+2)+1, where (2j2+3j+2) is a memeber of the natural numbers. This means that when n is odd, n2+n+3. Is this ok? Thanks for the help!