PEI Math 521A Practice Questions - Secondary Mathematics Assessment - Math 521A - Prince Edward Island Exam

Let the numbers be $2n+1$ and $2m+1$. Their sum is $(2n+1)+(2m+1) = 2n+2m+2 = 2(n+m+1)$, which is divisible by 2. Test $3+5=8$ and $7+9=16$. Since 8 and 16 are even, all sums of two odd numbers must be even. Let the numbers be $n$ and $n+2$. Their sum is $2n+2 = 2(n+1)$, which is even. Assume the sum of two odd numbers is odd, then find that $3+3=6$, which contradicts the assumption.