When a is a factor of a number b, then b is divisible by a. For example, 3 is a factor of 12, so 12 is divisible by 3. We will use this concept in the proof in this post.
Notice that the sum of the following consecutive odd numbers.
11 + 13 = 24
9 + 11 = 20
25 + 27 = 52
101 + 103 = 204
Notice that the sum is divisible by 4. Now, we can make a conjecture that the sum of two consecutive numbers is divisible by 4.
Theorem: The sum of two consecutive odd numbers is divisible by 4. Continue reading