Difference between revisions of "2024 IMO Problems/Problem 2"

Line 3: Line 3:
 
holds for all integer <math>n\ge N</math>.
 
holds for all integer <math>n\ge N</math>.
  
 +
==Video Solution==
 +
https://www.youtube.com/watch?v=VXFG1t_ksfI (including motivation to derive solution)
 
==Video Solution(Fermat's little theorem,In English)==
 
==Video Solution(Fermat's little theorem,In English)==
 
https://youtu.be/QTBcTtY46HI
 
https://youtu.be/QTBcTtY46HI
 
==Video Solution(Fermat's little theorem,In Chinese)==
 
==Video Solution(Fermat's little theorem,In Chinese)==
 
https://youtu.be/8WOff2j0giY
 
https://youtu.be/8WOff2j0giY
==Video Solution==
+
 
https://www.youtube.com/watch?v=VXFG1t_ksfI (including motivation to derive solution)
 
  
 
==See Also==
 
==See Also==
  
 
{{IMO box|year=2024|num-b=1|num-a=3}}
 
{{IMO box|year=2024|num-b=1|num-a=3}}

Revision as of 20:21, 29 August 2024

Find all positive integer pairs $(a,b),$ such that there exists positive integer $g,N,$ \[\gcd (a^n+b,b^n+a)=g\] holds for all integer $n\ge N$.

Video Solution

https://www.youtube.com/watch?v=VXFG1t_ksfI (including motivation to derive solution)

Video Solution(Fermat's little theorem,In English)

https://youtu.be/QTBcTtY46HI

Video Solution(Fermat's little theorem,In Chinese)

https://youtu.be/8WOff2j0giY


See Also

2024 IMO (Problems) • Resources
Preceded by
Problem 1
1 2 3 4 5 6 Followed by
Problem 3
All IMO Problems and Solutions