You may already know that 1+2+3+4+5=15. Let's try five other consecutive integers: 14+15+16+17+18=80. How about -1+0+1+2+3=5? We might guess that the sum of 5 consecutive integers is divisible by 5. That turns out to be true. Maybe the sum of n consecutive integers is divisible by n. That turns out not to be true: 1+2 is not divisible by 2.

Question: When is the sum of n consecutive integers divisible by n, and when is it not divisible by n?

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