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...") |
(→Video Solution（Fermat's little theorem，In Chinese）) |
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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>. |
| + | |||
| + | ==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== | ||
| + | |||
| + | {{IMO box|year=2024|num-b=1|num-a=3}} | ||
Latest revision as of 20:50, 30 September 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 
.
Contents
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 Chinese）
Video 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 | ||
