Question

Suppose you have the following question:
The sum of x consecutive odd integers is y.
Find the smallest integer.
\[\sum_{n=0}^{x-1}a+2n = y\]

How would you account for the fact that a must be odd? (consecutive even integers also have a difference of 2)
Or is there not always an answer to a question like this?
(Sorry, closed the question before by accident)

Answer 1

any odd integer can be represented as:\[2m+1\]for \(m=0,1,...,\infty\)