Difference between revisions of "1973 IMO Problems/Problem 5"
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Revision as of 18:42, 25 October 2014
is a set of non-constant functions of the real variable of the form and has the following properties:
(a) If and are in , then is in ; here .
(b) If is in , then its inverse is in ; here the inverse of is .
(c) For every in , there exists a real number such that .
Prove that there exists a real number such that for all in .