Presenter Information

John Arico, Mathematics

Faculty Sponsor(s)

Emma Wright

Abstract

The final question 1988 International Math Olympiad in Melbourne Australia, presented to the world’s best and brightest young minds, would evolve to become one of most difficult questions in Mathematics. Of the 260 participants, only eleven were able to solve Question Six perfectly in the given amount of time, proving too difficult even for future Field’s Medalist Terence Tao. Question Six simply states “Let a and b be positive integers such that ab + 1 divides a2 + b2. Show that the resulting integer is a perfect square”. This research explores a definitive solution to the infamous question, and features questions utilizing a similar train of thought, featuring an emergent proof technique that is new to the world of Mathematics.

Location

Hartman Union Building Courtroom

Start Date

5-2-2019 2:00 PM

End Date

5-2-2019 3:00 PM

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May 2nd, 2:00 PM May 2nd, 3:00 PM

The Legend of Question Six

Hartman Union Building Courtroom

The final question 1988 International Math Olympiad in Melbourne Australia, presented to the world’s best and brightest young minds, would evolve to become one of most difficult questions in Mathematics. Of the 260 participants, only eleven were able to solve Question Six perfectly in the given amount of time, proving too difficult even for future Field’s Medalist Terence Tao. Question Six simply states “Let a and b be positive integers such that ab + 1 divides a2 + b2. Show that the resulting integer is a perfect square”. This research explores a definitive solution to the infamous question, and features questions utilizing a similar train of thought, featuring an emergent proof technique that is new to the world of Mathematics.