Once in a Millennium (Math Chat)
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Frank Morgan, MAA Online  
Challenge: The year 2000 can be represented as the sum of consecutive integers: 2000 = 398 + 399 + 400 + 401 + 402. The year 2001 can be represented as the sum of consecutive integers: 2001 = 1000 + 1001. In fact, every year in the millennium from 2000 to 2999 can be represented as the sum of consecutive integers, except one year. Which year cannot be represented as the sum of consecutive integers?  


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