2024 IMO Problems/Problem 2

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

Video Solution

https://youtu.be/5SZUbbxoK1M

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