2019 IMO Problems/Problem 4
Problem
Find all pairs of positive integers such that
Solution 1
! = 1(when = 1), 2 (when = 2), 6(when = 3)
(when = 1), 6 (when = 2)
Hence, (1,1), (3,2) satisfy
For = 2: RHS is strictly increasing, and will never satisfy = 2 for integer n since RHS = 6 when = 2.
It remains to prove that these are the only pairs that satisfy.
~flamewavelight and phoenixfire