Difference between revisions of "1990 IMO Problems/Problem 4"
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4. Let <math>\mathbb{Q^+}</math> be the set of positive rational numbers. Construct a function <math>f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}</math> such that <math>f(xf(y)) = \frac{f(x)}{y}</math> for all <math>x, y\in{Q^+}</math>. | 4. Let <math>\mathbb{Q^+}</math> be the set of positive rational numbers. Construct a function <math>f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}</math> such that <math>f(xf(y)) = \frac{f(x)}{y}</math> for all <math>x, y\in{Q^+}</math>. | ||
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+ | [[Category:Olympiad Algebra Problems]] | ||
+ | [[Category:Functional Equation Problems]] |
Revision as of 07:44, 19 July 2016
4. Let be the set of positive rational numbers. Construct a function such that for all .