4. Show that if n is any integer, then n^2 3n 5 is an odd integer

Suppose the n is odd If n is odd, then n^2 will be odd If n is odd, then 3n will be odd We know that 5 is odd So, odd + odd + odd = odd Suppose the n is even If n is even, then n^2 will be even If n is even, then 3n will be even We know that 5 is odd So, even + even + odd = odd Hence n^2 + 3n + 5 is always odd