Question: Step by step 11. Consecutive Counting [15 points] A positive integer h is happy if the sum of any h consecutive integers is divisible by

Step by step

11. Consecutive Counting [15 points] A positive integer h is happy if the sum of any h consecutive integers is divisible by h. For example, 203 is happy if the number 1 + 2+ 3+ ... + 203 is divisible by 203, and the number 2+3+4+ ... + 204 is divisible by 203, and so on. Which positive integers are happy? Is it all of them? None of them? Only the even ones? Only those that are large enough? Something else? Choose one of the following three propositions, and then give a proof of the proposition you choose: . All positive integers are happy. . No positive integers are happy. . Some positive integers are happy, and others are not. A positive integer k is happy if and only if (if you choose this option, fill in the blank to complete a proposition)

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