The difference is 2003.
The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).
The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).
Knowing this, plug 2003 for n,
SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003
The difference is 2003.
A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.
Learn more about Even numbers here: https://brainly.com/question/251701
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