2019 USAJMO Problems/Problem 2
Revision as of 20:57, 18 April 2019 by Brendanb4321 (talk | contribs) (Created page with "==Problem== Let <math>\mathbb Z</math> be the set of all integers. Find all pairs of integers <math>(a,b)</math> for which there exist functions <math>f:\mathbb Z\rightarrow\m...")
Problem
Let 
be the set of all integers. Find all pairs of integers 
for which there exist functions 
and 
satisfying ![\[f(g(x))=x+a\quad\text{and}\quad g(f(x))=x+b\]](http://latex.artofproblemsolving.com/d/6/9/d69627a699096287d1de16796019aacb2c1c9e9a.png)
for all integers 
.
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
See also
| 2019 USAJMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
