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

(Ph.D degree, IMO coach,https://www.youtube.com/@math000)
Line 2: Line 2:
 
<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>.
 +
 +
==Video Solution(Fermat's little theorem,In English)==
 +
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

Revision as of 17:22, 10 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(Fermat's little theorem,In English)

https://youtu.be/QTBcTtY46HI

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

https://youtu.be/8WOff2j0giY

Video Solution

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

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