IMO Shortlist 2007 problem N6

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2. travnja 2012.
Let k be a positive integer. Prove that the number (4 \cdot k^2 - 1)^2 has a positive divisor of the form 8kn - 1 if and only if k is even.

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
Izvor: Međunarodna matematička olimpijada, shortlist 2007