# Sums of Consecutive Integers

**Algebra**Level 5

How many integers \(1 \leq N \leq 1000\) can be written both as the sum of \(26\) consecutive integers and as the sum of \(13\) consecutive integers?

**Details and assumptions**

The consecutive integers are allowed to be a mix of negative integers, 0 and positive integers (as long as they are consecutive).