February 9–February 15, 2010
Problem
Show that for every integer x, there is some integer y so that (y2 - 2)/(x4 + 1) is also an integer.
Submit your solution to challenge[at]math.washington.edu.
Prize
The winner of this week's Challenge Problem receives a gift certificate for Baskin Robbins Ice Cream!
Rules
The Challenge Problem is posted every Tuesday (every other Tuesday over the summer). Solutions can be submitted until noon of the next Monday. Anyone may participate. The winner is drawn from the pool of correct solutions, with preference given to solutions that are better than others (for instance, an exact result over a floating point result, etc.); to undergraduate students over graduate students over faculty; and to people who have not won a prize.
For questions, comments, or suggestions for future challenge problems, or to be added/removed from the email list: please email challenge[at]math.washington.edu.
The challenge problem is maintained by Jonathan Cross, Lucas Koepke, Hoyt Koepke, Roddy Theobald, and Alexander Volfovsky.