Difference between revisions of "1998 IMO Problems/Problem 6"
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Determine the least possible value of <math>f(1998),</math> where <math>f:\Bbb{N}\to \Bbb{N}</math> is a function such that for all <math>m,n\in {\Bbb N}</math>, | Determine the least possible value of <math>f(1998),</math> where <math>f:\Bbb{N}\to \Bbb{N}</math> is a function such that for all <math>m,n\in {\Bbb N}</math>, | ||
<cmath>f\left( n^{2}f(m)\right) =m\left( f(n)\right) ^{2}. </cmath> | <cmath>f\left( n^{2}f(m)\right) =m\left( f(n)\right) ^{2}. </cmath> | ||
| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=1998|num-b=5|after=Last Question}} | ||
[[Category:Olympiad Algebra Problems]] | [[Category:Olympiad Algebra Problems]] | ||
[[Category:Functional Equation Problems]] | [[Category:Functional Equation Problems]] | ||
Revision as of 22:54, 18 November 2023
Problem
Determine the least possible value of 
where 
is a function such that for all 
,
![\[f\left( n^{2}f(m)\right) =m\left( f(n)\right) ^{2}.\]](http://latex.artofproblemsolving.com/2/a/c/2ac108868d9b31654ca95e1ed205902c83a04cf2.png)
Solution
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See Also
| 1998 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
| All IMO Problems and Solutions | ||
