2019 USAJMO Problems/Problem 2
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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 | ||
