Math Puzzle

If you have so much time on your hands that you’ve ended up at this blog, here is a math puzzle I made up…

A broker is looking at three stock prices and notices a funny relationship. The three prices are all three-digit numbers. By subtracting the first number from the second number, she gets the same result as subtracting the second number from the third number. By subtracting the inverse of the first number from the inverse of the second number, and subtracting the inverse of the second number from the inverse of the third number, she still receives the exact same answer. Finally, each of the three numbers, minus its inverse, yields the same number (although a different number from the proceeding two operations).

What three numbers was she looking at? (NOTE: if you solve this without using palindromes, the solution is very elegant)

Email me your answer and I will send you a prize!*

 

*I do not have any prizes.  But you will have my heartfelt admiration.