2020 CAMO Problems/Problem 1
Problem 1
Let (meaning
takes positive real numbers to positive real numbers) be a nonconstant function such that for any positive real numbers
and
,
Prove that there is a constant
such that
for all positive real numbers
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Because , we can find that
It's obvious that if there exists two real numbers
and
, which satisfies
and
Then, for ,
,
Then,
The fraction is also satisfies for $f(x+y)
Then, we can solve this problem using mathematical induction
~~Andy666
See also
2020 CAMO (Problems • Resources) | ||
Preceded by First problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All CAMO Problems and Solutions |
2020 CJMO (Problems • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All CJMO Problems and Solutions |
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