Difference between revisions of "2024 IMO Problems/Problem 2"
(Created page with "Find all positive integer pairs <math>(a,b),</math> such that there exists positive integer <math>g,N,</math> <cmath>\gcd (a^n+b,b^n+a)=g</cmath> holds for all integer <math>n...") |
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Find all positive integer pairs <math>(a,b),</math> such that there exists positive integer <math>g,N,</math> | Find all positive integer pairs <math>(a,b),</math> such that there exists positive integer <math>g,N,</math> | ||
<cmath>\gcd (a^n+b,b^n+a)=g</cmath> | <cmath>\gcd (a^n+b,b^n+a)=g</cmath> | ||
| − | holds for all integer <math>n\ge N</math> | + | holds for all integer <math>n\ge N</math>. |
Revision as of 21:34, 16 July 2024
Find all positive integer pairs 
such that there exists positive integer 
![\[\gcd (a^n+b,b^n+a)=g\]](http://latex.artofproblemsolving.com/1/f/4/1f4ed3e8276279d224eb603b60082fa40dd2e0af.png)
holds for all integer 
.
