mathematics - Non-Pythagorean coins (Part 1)

To make payments, the Non-Pythagoreans use coins in three denominations of 999, 1000, and 1001 Oboloi. What is the largest integer amount of Oboloi that can not be represented by using these three types of coins?

Comment 1: valid representations use non-negative numbers of coins

Comment 2: Pythagorean coins

Answer

I think the answer is

498500
because $498500=498\times999+998$ and in modular arithmetic we have $1000\equiv1\pmod{999}$ and $1001\equiv2\pmod{999}$, so the remainder of $998$ cannot be made by fewer than $499$ additions of positive numbers less than or equal to $2$.