Difference between revisions of "1999 IMO Problems/Problem 4"
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Determine all pairs <math>(n,p)</math> of positive integers such that | Determine all pairs <math>(n,p)</math> of positive integers such that | ||
| − | <math>p</math> is a prime, <math>n</math> not exceeded <math>2p</math>, and <math>(p-1)^{n}</math> is divisible by <math>n^{p-1}</math> | + | <math>p</math> is a prime, <math>n</math> not exceeded <math>2p</math>, and <math>(p-1)^{n}+1</math> is divisible by <math>n^{p-1}</math> |
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=1999|num-b=3|num-a=5}} | ||
Latest revision as of 23:56, 18 November 2023
Problem
Determine all pairs 
of positive integers such that
is a prime, 
not exceeded 
, and 
is divisible by 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1999 IMO (Problems) • Resources | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
| All IMO Problems and Solutions | ||
