Problem: The number of sets of two or more consecutive positive integers whose sum is , is
Answer Choices:
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Solution:
Either the number of consecutive integers in a set will be odd or aven. If odd, let their number be and their average , the middle are. Then so that can only be or . If , then and so that the integers are . If and which is imponsible because the integers must be positive. If the number of consecutive integers is an even number , let their average thalf way between the middle palr) be denoted by . Then . For and the middle pair are so that are the integers. For no other integer , are the middle pair and positive integers. The two displayed are the only sets of pondive integers whose sum in .