2017 IMO Problems/Problem 2
Let be the set of real numbers , determine all functions such that for any real numbers and
Looking at the equation one can deduce that the functions that will work will be linear. That is, a polynomial of at most a degree of 1.
Thus, is in the form
From [Equation 1] we have,
From [Equation 2] we have,
From [Equation 3] we have,
When , , then
When , , then since , then
When , , then since , then then which gives these two functions:
and , which with provide all the three functions for this problem.
~Tomas Diaz. firstname.lastname@example.org
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
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