Difference between revisions of "1998 IMO Problems/Problem 6"
m |
Robindabank (talk | contribs) (→Solution) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | |||
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> | ||
| + | ==Video Solution== | ||
| + | https://www.youtube.com/watch?v=vOExNCV8jGQ | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{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]] | ||
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)
