The number can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of . Find the smallest of these consecutive integers.

Source: NCTM Mathematics Teacher 2008

**SOLUTION
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The exponents of the prime factors yield the number of factors of 2008

Number of terms in the sum is twice the number of factors

Suppose the sum of consecutive integers starts with

How do we know the result is unique? Numbers of the form , where is prime, can be written as the sum of consecutive positive integers in exactly one way. fits this description.

**Answer**:

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