HMMT February

Algebra Difficulty 4.8 AIME Find the answer

Let $x=2001^{1002}-2001^{-1002}$ and $y=2001^{1002}+2001^{-1002}$ . Find $x^{2}-y^{2}$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

-4.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.