Difference between revisions of "1990 IMO Problems/Problem 4"

Revision as of 12:46, 30 January 2021

Problem

Let $\mathbb{Q^+}$ be the set of positive rational numbers. Construct a function $f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}$ such that $f(xf(y)) = \frac{f(x)}{y}$ for all $x, y\in{Q^+}$ .

Solution

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-. 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>.
+==Problem==
+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>.
+==Solution==
+{{solution}}
+== See Also == {{IMO box|year=1990|num-b=3|num-a=5}}
 [[Category:Olympiad Algebra Problems]]
 [[Category:Functional Equation Problems]]

1990 IMO (Problems) • Resources
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Difference between revisions of "1990 IMO Problems/Problem 4"

Revision as of 12:46, 30 January 2021

Problem

Solution

See Also