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Function Finding From Floor (
Posted on 20160930
)
Find all functions f:R > R such that:
f(floor(x)*y) = f(x)*floor(f(y)) holds for all x and y.
Prove that no other function satisfies the above relationship.
No Solution Yet
Submitted by
K Sengupta
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(1 votes)
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Solution (spoiler)
 Comment 1 of 2
Let y = 0.
Then f(0) = f(x)*floor(f(0))
This means that f(x) must be a constant. Call it c.
Then, for all x and y,
c = c*floor(c)
Either c = 0 or floor(c) = 1.
So c can be 0 or c can be in [1,2) (i,e, >=1 and <2)
Posted by
Steve Herman
on 20161001 12:45:56
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