2021 AIME I Problems/Problem 10
Problem
Consider the sequence 
of positive rational numbers defined by 
and for 
, if 
for relatively prime positive integers 
and 
, then
![\[a_{k+1} = \frac{m + 18}{n+19}.\]](http://latex.artofproblemsolving.com/f/8/3/f8375cf3493310402a251be2df8e930251bd5a5d.png)
Determine the sum of all positive integers 
such that the rational number 
can be written in the form 
for some positive integer 
.
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
