In the previous problem you were asked to prove that the sum of any three consecutive

Chapter 0, Problem 15

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In the previous problem you were asked to prove that the sum of any three consecutive integers is divisible by three. Note, however, that the sum of any four consecutive integers is never divisible by four. For example, 10 C 11 C 12 C 13 D 46, which is not divisible by four. For which positive integers a is the sum of a consecutive integers divisible by a? That is, complete the following sentence to give a true statement: Let a be a positive integer. The sum of a consecutive integers is divisible by a if and only if . . . . You need not prove your conjecture.