Select an easier sub-problem and you get an IMO problem
Source: IMO Shortlist 2007, N6
July 13, 2008
quadraticsnumber theoryIMOIMO 2007Vieta JumpingDivisibility
Problem Statement
Let be a positive integer. Prove that the number (4 \cdot k^2 \minus{} 1)^2 has a positive divisor of the form 8kn \minus{} 1 if and only if is even.
[url=http://www.mathlinks.ro/viewtopic.php?p=894656#894656]Actual IMO 2007 Problem, posed as question 5 in the contest, which was used as a lemma in the official solutions for problem N6 as shown above.
Author: Kevin Buzzard and Edward Crane, United Kingdom