Difference between revisions of "2019 IMO Problems/Problem 4"
Toinfinity (talk | contribs) (Created page with "Find all pairs <math>(k,n)</math> of positive integers such that <cmath>k!=(2^n-1)(2^n-2)(2^n-4)\dots(2^n-2^{n-1}).</cmath>") |
|||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | |||
Find all pairs <math>(k,n)</math> of positive integers such that | Find all pairs <math>(k,n)</math> of positive integers such that | ||
<cmath>k!=(2^n-1)(2^n-2)(2^n-4)\dots(2^n-2^{n-1}).</cmath> | <cmath>k!=(2^n-1)(2^n-2)(2^n-4)\dots(2^n-2^{n-1}).</cmath> | ||
| + | |||
| + | ==Solution 1== | ||
Revision as of 13:46, 15 December 2019
Problem
Find all pairs 
of positive integers such that
![\[k!=(2^n-1)(2^n-2)(2^n-4)\dots(2^n-2^{n-1}).\]](http://latex.artofproblemsolving.com/7/c/a/7ca521b92d40def7f320702893c01502439174e8.png)
