Let
be a positive integer. Prove that the number
has a positive divisor of the form
if and only if
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
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![(4 \cdot k^2 - 1)^2](/media/m/a/4/1/a41fb4fe7b3b1dbfbf2b295cd6dbf907.png)
![8kn - 1](/media/m/4/6/2/4623eb27d1bf307bd92fb51dc2ae47c8.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
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