A student wants to prove that the sum of two consecutive integers is always odd. Which way of writing the two integers leads to a complete proof?

Answer and explanation

Correct answer: A. Let them be and for an integer

  1. Step 1: Any two consecutive integers can be written as and for some integer , so this covers every case.
  2. Step 2: Their sum is , which is one more than an even number, hence odd.
Answer
Let them be and for an integer .
Why not the others: One example proves nothing; and are consecutive even numbers, not consecutive integers; and are not consecutive; and differ by 2.

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